All right, good morning and welcome to this week's edition of Encompass Live. I am your host, Krista Porter, here at the Nebraska Library Commission. The Encompass Live is the Commission's weekly webinar series where we cover a variety of topics that may be of interest to libraries. We broadcast the show live every Wednesday morning at 10 a.m. Central Time, but if you're unable to join us on Wednesdays, that's just fine. We do record the show as we are doing today, and it is then posted onto our website where you can watch it at your convenience. And I'll show you at the end of the day show where all our archives are and how to navigate those. Both the live show and the recordings are free and open to anyone to watch, so please do share with your friends, family, neighbors, colleagues, anyone you think might be interested in any of the topics we have on the show. The Nebraska Library Commission, for anyone listening who's not from Nebraska, but I think most people today's show would be Nebraska people, we provide services to all types of libraries in the state. So you will find things on our show for public academics, K-12, museums, corrections, archives, anything and everything. Really, our only criteria is that it is something for libraries, something libraries are doing. We bring in guest speakers, talk about cool things they're doing at their libraries, services and resources. We think might be of interest to them, things we're doing here at the commission for people. So there's a real huge range of things that we do here on the show. Before we get into today's show, I do want to quickly highlight something here on our library commission website. If you go to our commission's main webpage, nlc.nabrasca.gov, we are still right in the height still of the COVID-19 pandemic. And here at the Nebraska Library Commission, we are attempting to gather as many resources as we can to help our libraries work through this. We have a post here at the top of our webpage. It is pinned there, so it'll always be at the top of all of our blog posts, links to good information. And we have a list that we're attempting to keep up to date as well as we can for what's happening with the Nebraska libraries. Our library is open, is it closed, limited hours, different accommodations they're making, Wi-Fi in the parking lot, whatever. And libraries re-closing, we've now had that across the country where in many locations, places have reopened too soon, and there are new outbreaks. So we try to keep that up to date, so check and see if your library is on there. Remember, this is just Nebraska libraries, and make sure we have the most up-to-date info. If you don't, give us a call, send us an email, and we can update that for you. I just want to show you here on our pandemic blog post, we do have a form you can use to update that list. And then we have a link here for a whole bunch of different resources that our staff has gathered. All sorts of different things you might need, how to homeschool my kids and employment, et cetera. But I just wanted to highlight the page of out libraries, where we have organized things into all the different topics you might need more information about. As we hear of new research that's been done, new webinars that have been put on, new resources, we add them to the page, so it's always being updated. We do have guidelines here about how you could reopen your library, how to keep clean things, how to deal with books, how to hold meetings, et cetera, et cetera. Examples of other library policies regarding reopening and being safe. So please do keep it on this page, check into it for any information you may be looking for regarding COVID-19, the pandemic, and how libraries can work with it. So I am going to make our presenter, our speaker for today, the presenter. So, Susan, you should see a pop-up giving you screen control. Okay. You should be able to show your screen. There we go. There we go. All right. So this morning, as I mentioned before, we have a Nebraska Library Commission staff. Susan Nisley, good morning, Susan. Good morning. She's just down the hall from me in her office. And she's going to talk about some great deals you can get if you're here in Nebraska Library on a lot of things that we have here at the Library Commission. The lists are just exhaustive. It's awesome. So I'll just hand it over to you, Susan, to go ahead and take it away. Okay, great. Thanks, Christa. As Christa said, my name is Susan Nisley, and I work in the Technology and Access Services Department. I have been here since December 1998, so for a while, and I have been working with this program since that time. It's one of my responsibilities. And this is a program that, as I said, has been going on for quite a while in various forms. But we do like to, a lot of people know it and participate in it, but we do have staff turnover, staff changes. And so it's always good to have a presentation periodically where we present it again just to make sure that we catch people who may not have heard about it before. And so that is why we're doing this presentation today. I always like to start out just emphasizing the mission of the Nebraska Library Commission. In particular, when I talk about the discount program, because I think our discount program really aligns with our mission. And so if you will indulge me, I'm going to go ahead and read the mission statement. The mission of the Nebraska Library Commission is statewide promotion, development, and coordination of library and information services. And as the state library agency, the commission is an advocate for the library and information service needs of all Nebraskans. One of the challenges that we face in Nebraska is that we do have a relatively small population. And we don't necessarily have an even distribution of population. So we do have a lot of small libraries serving communities with small populations. And that means that budgeting is always a challenge. If you are primarily funded based on the population you serve and you're serving a small population, you're not going to have as large a budget as bigger libraries. So again, anything we can do to try to make services more affordable to more libraries so that they can then make those services available to their patrons, Nebraska residents, that's all in service for our mission. So that is really behind this program and we are really able to be, I think, through this program and advocate for library and information service needs for Nebraskans because we're in a good position to advocate for our libraries with the vendors. Again, we have smaller libraries in our state than some other states. And many of the vendors don't really have a good understanding of that size differential. So when they say small library, they sometimes are thinking, you know, a library with 20,000 pop served as a small library. And so they may give us pricing and they say, Oh, your smallest libraries, anybody serving 20,000 people or fewer, here's their price. Well, in Nebraska, the budget of a library that serves 20,000 is going to be a lot larger than the budget of a library that serves 1000 or 500. And so, you know, those libraries aren't necessarily going to be able to spend the same amount on product or service. And so, any of these large companies and it's been historically a ongoing struggle for us. They're right of a small library is not the same thing as reality. No, absolutely not. And I know when you used to work with OCLC, that was a constant battle. But with OCLC, what's a small library? I've sent vendors census data. I've sent them information. Our Nebraska Department of Education has a directory of school districts and they provide statistics about how many students are served by a school district and how many students are in each grade. And I always remember specifically, I think it's Arthur County. I think it's the smallest population county in Nebraska, maybe. And at one point it had, it was under 500 total population for the county. And we were trying to get, I think, a price quote for the school. Well, when you look at, there's one school district there and when you look at the population or the number of students in grades 7 through 12, it was like 56 or something. And these vendors are used to providing pricing for high schools that serve 1,000, 2,000 students. And so it was not working at all. And I don't think that the vendor believed me initially when I was talking about the size. So like I said, I had to, I actually sent her some data. We're not just making this up. Yeah, your statistics that show this is true. So that's a role that I can play as an advocate for our special needs. We also here have access to all of the library statistical data that you submit each year. So I can sometimes say, this is an example of the type of operating budget that a library has.  So, you know, I can wield that information for our, and your benefit. So that sort of is a little bit of a background on what our role is and how we can hopefully help get you access to products and make them a little bit more affordable possibly. Just a little bit of history. I would say the seeds of this program started back in the summer of 1995. If we can all remember back that far, the internet was around. If libraries had online products, sometimes they were CD-ROMs. There were some online databases available, but not all, maybe not a majority of libraries had access to them. Larger publics, academics maybe. So this was all a brand new world. And there was an article in an old newsletter that it was archived on our website. And it talks about the fact that the Nebraska Library Commission Steering Committee in the summer of 1995 was talking about the possibility of offering a statewide first search database trial. And they had identified first search as a service that would further our mission. And so the first statewide database trial for first search was February 1st through April 30th, 1996. And we actually had 155 libraries participate. Back then, as I said, this was all brand new. And so having an organization like the Nebraska Library Commission sort of facilitate the trial and publicize it and make it easy for libraries to participate, I think really helped, especially the smaller libraries that were maybe a little bit more hesitant, that wouldn't necessarily contact a vendor themselves and say, I want to set up a trial. So that's kind of how the program got its start. And we've continued to offer database trials over the years. We still have a mailing list that we post information on about database trials when a vendor offers them. And so I will point out more information about that, that mailing list later on in the session today. But again, this is when the program kind of got off the ground. And there are basically, I would say, three strands to this program. There are discounts on databases and e-resources. And this is the part of the program that I think most people or more people are aware of. More people, more libraries participate in this part of the program. It's certainly something that I spend the more active time involved in because it involves getting information out about products to libraries, managing subscriptions and renewal. So it's something that I'm constantly involved in and working with participating libraries on and vendors on. So that's probably the, like I said, the most well-known component of the program. We also have a discount page that lists discounts on books and supplies. And we have regular discounts on information today, conferences like computers and libraries and Internet Librarian. And so I don't think those are as well known. They don't require the kind of active, constant interaction that the database and e-resources program requires. And so I don't have as good a sense of how many libraries participate in them just because once the information is out there, libraries interact directly with the vendors or the conference and don't go through me. So those don't get, I think, as much press and may not be as well known. And again, that's why we have programs like this one today to make sure that people are aware of them. This is a screenshot and I'm going to momentarily switch to a live sharing of my web browser so we can look at this live. But this is the main index page for the discounts on databases and e-resources. So let me go ahead and see if I can go there live. And let's see. There you go. Yep. OK, there we go. This is the main Nebraska Library Commission home page. And so I thought we'd start here just so I can show you a quick shortcut way to get there. If you look at the menu along the left side of the screen, you'll see one of the categories is discounts and group purchases. Once you hover over it, you get a fly out and the top category is discounts. And you'll see there's discounts on books and supplies, discounts on conferences and discounts on databases and resources. So that's always a quick way to get to any one of these three pages. So I'm going to click on databases and resources. And I'll just point out once you're on one of these three pages, there are always links at the top to the other two discount pages. So discounts on books and supplies and discounts on conferences. So there is a little bit of circularity there. This page is obviously an alphabetical list, and it includes vendor names. So you'll see vendor listed like Britannica Online. You'll also see listed names of specific products. So, for example, Britannica Online Academic Edition, Britannica Online Public Library Edition. Some products obviously have the vendor's name in the database name. Others don't. So this is sort of a cross-referenced books in print. It's a ProQuest product, and so that will take you to the ProQuest page. So again, I don't know that I have every single database listed on this page, but if it's a product that a lot of libraries subscribe to, and I think it might be a way that people would try to look up information, I will list the specific database name on this page, as well as the vendor. Again, sometimes people don't know. It's sometimes, you know, you don't always know what who's the vendor. You just know the database name. The other challenge with this page is products move around from one vendor to another. Sometimes one vendor purchases a product that is previously available through a different vendor, so that always gets a little bit challenging. And databases change names, too. And so then there's always that transition period. It's if you're used to calling a product by one name, and then suddenly it's going by another name. Sometimes I'll leave both names included in this list for a while until we all wean ourselves over to the new name. So again, this page isn't perfect, but it does attempt to get you to where you need to be. So just as an example, I'm going to go to the Britannica online page and use it to give you an idea of the kind of information you typically will find on a database or a vendor specific page. And it varies by vendor. But typically I will have a list of at least the most prominent databases that are offered from a particular vendor at a discount. So I will list the databases. I'll include a brief description of the database. And then I will often include a link to the vendor page where they'll provide more information about that specific database. There will be a pricing section. And it really varies from vendor to vendor, whether they allow pricing to be posted on the website. I would say the majority do not because they want that information. They don't want their competitors to get that information. If a vendor allows pricing to be posted, I will put it up on the page. So in this example, you can see specific pricing for each of the databases. And you'll also see some waiting factors for how to compute your pricing. So for your colleges, use 100 percent of their full time equivalent enrollment number in order to calculate their price. Two year colleges use 75 percent of their full time equivalent enrollment numbers. Public libraries use 7 percent of their population served. And then in this particular case, pricing is per FTE or per pop served. So you just have to multiply the cost per FTE times your total FTE or pop served. It's fairly typical that libraries or vendors will have minimum prices. So if you've got a small pop served and your price calculates out to less than $540 in this particular instance, you would have to pay the $540. So in this particular case, it's really nice because you can come here and you can get pricing right away. In other cases, it will just say contact Susan Nicely for pricing and it will have a link that will let you send an email to me. And I'm in some cases, I may have a price list, a discounted price list that the vendor sent me and I can look the price up and provide it to you. In other cases, the vendor wants me to contact them directly each time a library wants a price quote and they will usually want to know what's the pop served, if it's a public library or how many students, if it's a school or FTE for an academic. And then they'll provide pricing discounted pricing and I'll pass that back onto the library. So that's how the pricing section works. There's typically a subscription term listed. We try to keep the database subscriptions on several common terms. For example, we have a lot of subscriptions that run from July 1st through June 30th. That's our fiscal year and it's a fiscal year for a number of libraries in the state. And so we try to do that so that we have sort of a specific time of the year when we're particularly busy with renewals. That doesn't always work out. You'll see that Britannica is on a June 1st through May 31st subscription term. And I think that is because we initially piggybacked with another library organization based out of Colorado on this particular discount. And this was a term that they'd already set. And so we just inherited that term. So anyway, you'll see what the sort of target subscription term is. If there's a deadline for ordering or renewal, that information will be there. Britannica is actually, I think, the only database now that we still have an online order form for. And the reason we're able to do an online order form is because the pricing is very concrete. You can see what your price is on the page and calculate it. And so we can get a form to uptake that information and submit it to us. In lots of cases, you'll be just directed to contact me and I'll make up an order form with your price on it and send it out to you to fill out and send back in. I will typically go out and look and see if I can find a tech support numbers or email addresses for this for the particular vendor in question. And if I can find that information, I will put that on the vendor page, links to where you would get usage statistics. And in this particular case, I've got there are separate access URLs for each of the Britannica databases. And so I've listed that. Again, this is a good example, but every vendor differs in terms of the kinds of information that wind up on their page. Case switching back to the slideshow. I just want to talk a little bit about some of the types of pricing discounts. We are able to arrange with the vendors. One typical type of discount is just a vendor will often give us a standard percentage discount off list price. And this can range anywhere from 5 percent to 25 percent. EBSCO is a good example. They just as a general rule because Nebraska does so much business with them, they will give any Nebraska library 5 percent off list price when they are going to subscribe to a database. If EBSCO has a particular product that they want to promote, maybe it's a new product that they've just acquired and they want to. Drum up business for it, they may approach us and they may ask us if we will publicize a trial and they may offer a more significant discount to libraries that sign up as new subscribers after that trial periods over. So they will come to us then when they they know that we have easy ways to communicate with multiple libraries across the state. And so in fate in return for us doing that, getting the information out, promoting a trial, soliciting inquiries and expressions of interest from libraries, they will offer an additional discount sometimes. Five percent I'm usually fairly disappointed with if we get a five percent off list price. If the price is fairly low, five percent doesn't amount to much. But if you've got, you know, a more expensive product, five percent adds up and can be a significant chunk of change. So, you know, we we we will take five percent versus zero percent. Once you get up to about twenty five percent off this price, you're really talking about some significant savings. So those are the kinds of discounts that we really feel good about when we're able to arrange. Another type of discount we've sometimes been able to arrange for Nebraska libraries is sometimes after talking to libraries about talking to vendors about the size of libraries in Nebraska. Sometimes we've been able to get them to offer special pricing just for small Nebraska libraries. And one example, a number of years ago, SIRS, the SIRS databases, we got special pricing that was just for schools serving fewer than 300 students. And so that really made the SIRS databases much more affordable to those smaller schools than they otherwise would have been and then some of their competitors were. So when we can get pricing that's really geared to the size of Nebraska libraries, that's really beneficial. A lot of times vendors want to offer discounts based on the number of participating libraries. And I would say this is probably the most difficult type of discount offer to deal with. We often have especially vendors that approaches for the first time and want to introduce and promote a new product and they want to try to get some new subscribers. They will come and they will say, well, if you can get up to 15 new subscribers will give you, you know, a 10 or 15 percent discount. Well, that the when I hear that my spirit always sinks because in Nebraska anymore, it's really hard to find 15 libraries that want to subscribe to the same product at the same time. Back in the early days of databases, when there weren't as many databases, not as many libraries subscribed to databases. Sometimes you could get a lot of libraries to come on board when they were ready to take the plunge, get into the online information sphere. Maybe you could get a whole bunch of new libraries to come on with a database, but now if libraries are going to be subscribing to databases, they're probably already subscribing to something. So it's a matter of dropping one product in order to subscribe to another. Some of the databases are more specialized. So finding 15 libraries that want to subscribe to, for example, a hobbyist database at a particular time, not necessarily going to happen in Nebraska based on our numbers. So these deals are harder to put together. They also require a lot more back and forth with libraries, just because it's a matter of you can't necessarily tell the library what the price is going to be until you know how many libraries are going to subscribe. And so as that number changes or as people drop out, the price changes constantly. And so it's a constant back and forth. The other thing about deals like this is sometimes they are more vulnerable to falling apart after the fact. So you might say you have between six and ten libraries that subscribe to a product and they get a 10 percent discount. Let's say you have six libraries. Well, what happens the next year if one of those libraries doesn't renew and then you're down to five? Some vendors are pretty good about continuing to allow the remaining libraries to continue to get the 10 percent discount. But there are others who are sticklers and will say, well, if you size of your group changes, then you may lose some of that discount. And so again, depending on the vendor that can be that's kind of a challenge. We also piggyback with other library networks. And sometimes we're able to piggyback on deals that they've organized there are networks out there that they're not based in state libraries like we are. They are independent organizations that have formed. They have similar missions to ours to try to coordinate library services for libraries to try to achieve discounts on products and subscriptions for libraries. But they're not state supported. So Lyricist is an example. They are based in Georgia and they work with they started out working primarily with libraries in the Southeastern United States. And sometimes more broadly, but they've been able to put together discounts on products like Lexus Nexus and Project Muse. And they've been able to work with other consortia, other state libraries, other networks across the United States. And by bringing all of those libraries from those different groups together, they've been able to achieve fairly significant savings on these products. So the benefit of partnering with another network is that they're able to achieve bigger discounts based on more participating libraries. Oftentimes, libraries that actually belong to these other networks do have to pay membership fees to belong. When we partner with one of these networks, our libraries don't necessarily don't have to pay that membership fee and they'll get the benefit of a discount. The only downside is that because these networks have to be self-sustaining, they usually will keep a portion of the discount back as a type of a as a they have to keep between membership fees and keeping part of the discount for themselves. That's how they sustain themselves, pay for staff, pay for rent, etc. So that may cut into the discount a little bit, but on the other hand, you're able to achieve a bigger discount because you've got more participating libraries. So usually we still come out ahead. Just another example of partnership. We've got, I think, two academic institutions that subscribe to ACM Digital Library and we partner with Minitex for that. With just two libraries interested in that product, we probably couldn't get much of a discount directly. But since Minitex is working with this particular product and they have a lot of libraries that they work with in Minnesota, South Dakota, North Dakota, we're able to take advantage of that as well. The last type of discount is probably the rarest, but when we're able to pull it off, it's really, really beneficial. It doesn't happen very often, but occasionally we've had vendors that have let us pull the population served of libraries that are interested in a particular product and we'll pay based on the total pop served and then we can proportionately divide up the price based on the proportion of population contributed by each of the libraries. So just a very rough example. Say you have a product and they say, if you serve a thousand or fewer pop served, you pay a thousand dollars. Well, if you've got four libraries and they each serve 250, if they approach the vendor on their own, they would fall into that zero to one thousand pop served category. They would each pay a thousand dollars. If we're allowed to pull the population served, the four libraries combined pop served as a thousand dollars. So they would just charge us a thousand dollars and then we could turn around and bill each library for 250. So again, it's very rare that a vendor does this, but we've had a couple of cases where that's happened and it's been a really great deal for our libraries and that's been a deal that's been ongoing. The one example, the best example is Learning Express from it's now an EBSCO product. But when we first started working with the product, it was independent. It was its own deal and they let us, the initial group of libraries that subscribe, they let us pool their populations and get pricing based on the total and then divide up the cost. So after that initial group and after EBSCO purchased the product, new subscribers that come on board have paid higher fees, much higher than the initial libraries paid, but I mean reasonable for a product like Learning Express. So we have some libraries out there that are fairly good sized but they're paying less than $200 for Learning Express because EBSCO's kind of grandfathered them in and they have a slight increase every time they renew, but because their initial price was so low, they're still under $600 for a product that other libraries are paying between a thousand and $2,000 for. So those are great when we're able to arrange those and that actually makes me think of another way in which we're sometimes able to benefit libraries. There are disadvantages to being in the same job for a long time, but there are also some advantages and one of the advantages I have since I've been doing this since 1998 is that I have a pretty good memory and I also have a pretty good email archive of old emails. I tend not to delete anything. Same, me too. Yep, it's very useful. You can still see, you'd be surprised what I still have and that was a long time ago. Yep, yep. So everyone, the vendor representatives tend to change every couple of years. So I've been working with the same vendor sometimes for 20 years, but over that timeframe, they may have gone through five or six different reps that I've dealt with. Every once in a while, a rep will come along and just in the past year, I think with CQ Press, a rep came to me and said, well, this is just some of your libraries are paying way below over 20, more than 20% off of list price. And so we're gonna have to work to get them back up to what we'd consider a reasonable discount. And so we're gonna have to increase their prices. And that just rang a bell with me that something was off and so I was able to go back and find out that in the early 2000s, they'd participate in a special promotion that involved purchasing access to the back files, perpetual access to back files. And along with that, they were guaranteed significant savings on ongoing subscriptions. So, I was able to send that information back to the vendor and say, this is why their prices are so much lower than what you would expect. And they were guaranteed this. And so, then they put a stop to that. So, I'm sure I don't remember everything and something slipped by me, but I do have that sort of institutional memory. And so sometimes I can wield that in libraries favor. I think this just kind of summarizes what I've already talked about. I guess I didn't talk about the centralized billing. One of the benefits that we argue to vendors of providing our libraries with discounts and working with us is that we will do centralized billing for them. So, if multiple Nebraska libraries participate in a deal and subscribe, instead of the vendor having to work with each of those libraries separately on their initial subscription and on renewals, they can just work with us. They can, for example, send us one bill. It can either be broken down by each individual library or they can just send us an invoice for the lump sum and we will pay them. And then we in turn turn around and we'll bill the individual libraries for the exact amount that their subscription costs. And then we do that with the renewals too. So when it comes time to send out renewal pricing, the vendor sends it to us and then we redistribute it to the libraries. We send out renewal forms, we send reminders, we send follow-ups, we track down an answer. So that streamlines things a little bit for the vendor and so that is one of the benefits that we offer vendors. This can also sometimes benefit, there's some benefits to libraries doing this. There are some libraries that have credits on file with us and so they can use those credits towards their bills. They can, sometimes they wanna be invoiced early based on spending funds before the end of our fiscal year, we can do that. Occasionally, there are libraries that need to delay payment a little bit because they need to wait until they're into a new budget cycle before they pay their bill. And as long as not everybody wants to do that at once, that's usually something that we can accommodate and let them go a little longer than the regular vendor might have. So we can be a little bit flexible like that. As I said, we try to maintain a couple of standard subscription terms, July 1st through June 30th and January 1st through December 31st. If a library wants to come on midterm, we try to get the vendor to pro-rate the subscription so that it'll end in one of the standard end dates and then the next time around, the library will be on the standard term. Sometimes that doesn't happen and so we do have, over time I'd say we probably are to the point now where we always, every month we probably have something coming up for renewal, that's just the way it goes. But we do still have the two times of a year that are the busiest for renewals approaching July and approaching January. Again, because we're a state agency, we don't have to make any money off of this process. We're able to pass on any discount we get to the library so that's one benefit that we have that some of the other networks that do similar things don't have. Just to give you a little snapshot of the database subscription program this past year, the discount program. So this is one of our fiscal years, July 1st 2019 to June 30th, 2020. We processed 443 individual subscriptions for 147 unique databases. We had 124 libraries participate and the total cost of all of those subscriptions was close to two and a half million dollars. And one thing I just calculated for my own amusement, you'll remember I mentioned that discounts range anywhere from 5% to 25% and so I just thought, okay, two and a half million. Let's say even if the 5% discount I don't particularly like, it just seems small and not very significant, but if you look at 5% of two and a half million, it's what 125,000, which is not chump change. So, and I'm sure we save more than that because a lot of the discounts are steeper than that. So that's a number to get to keep in mind when I'm feeling like a 5% discount is measly compared to what I want. Okay, moving on to the next discount on Books and Supplies, the second branch of the program, I'm gonna go ahead and again go back to our live webpage. And again, I can either click on Books and Supplies up here on the top of the Databases and E-Resources page or I can go over to the left and select it from the flyout menu. So this is our discounts on Books and Supplies page. It's got an alphabetical list of the different vendors on top and then as you scroll down, you will see more information about what they offer, what their discounts, what the discount is and how you go about getting it. The way this program works is usually the particular vendor or company will approach us and they'll say we'd like to promote our product to your members and they usually use the word members because they're used to dealing with other types of library consortia or networks. And they'll say we'd like to offer them a discount, can you publicize this? And so we will put that information up on this page. Usually when it's a brand new company, we'll send out a message on our trial mailing list, maybe post a notice on our blog to try to get the word out, but long-term the information lives on this page. Some of these discounts are issued updates every year. They will have an expiration date and I will usually put that as expiration date. Let me see if I can find one here. Yeah, Brodart here. So Brodart, this particular discount, the terms are valid through December 31st, 2020 and so late November, early December, I will either reach out to Brodart, they will reach out to me in order to update these terms and sometimes they'll just say, just extend the term until the next year, other times they'll have some updates. Oftentimes there will be a discount code that you will need to mention when you're ordering on the phone or if you're ordering online, there'll often be a place for you to enter the discount code in order to make sure that you get the discount. The one thing about this program is once the information's up there, you as the library take the information and then work directly with the company and so I am not as involved in the process. So again, I don't have a good sense as I do with the database program, how many libraries are benefiting from these discounts and I don't necessarily know how the process is going unless someone reports a problem, in which case then I can follow up with the company and make sure that either they follow their discount schedule that they provided us or I can update the terms if they've changed. So this program is a little bit more hands off and a little bit more outside of my central vision in terms of knowing what's going on with it. But as I said, that information is up there and available for you to look at at any time. There are companies that provide discounts on books, companies that provide discounts on library supplies, barcodes, I know just like we do with databases, we partner with, in one case, Minitex. They do tattle tape and security tape and they buy some of this stuff in bulk and then they're able to like redistribute it, repackage it in smaller amounts and sell it at a discount. So sometimes you'll be directed to one of those other networks to get your discount. Going back, let's see, that information's just a repeat of what I've already told you. So it's on the slide for your reference. Finally, we've been offering discounts on conferences back at least until 1997. And information today has sponsored a number of conferences. They sponsored computers and libraries, Internet Librarian. They used to also do Web Search University, which they'd offered discounts on that they haven't done that for a couple of years. And this just, this gives you an idea of what the discount would be on computers and libraries. The last time they had an actual in-person event, you could subscribe through us for 359 versus 549. So anytime you're going to one of those conferences, there's never a reason to pay the full price. A lot of librarians know that every year we offer discounts on this information. And so some of them know to contact me, maybe I haven't gotten the discount information yet, but I will have libraries reach out and say, we are gonna send a staff member to this conference, do you have the discount code yet? And so that's good that they're aware of it and that they're looking for it. When we get the discount, again, I always send a message to the trial mailing list and I'll usually post to our blog so that hopefully I'll catch the attention of people who maybe haven't been around as long and haven't sort of internalized the fact that that's available every year. This most recent year, it took them a while to get out information because they were going online. They're not having an in-person conference this fall. And so right now the offer is for, it's a combined computers and libraries and internet library and connect. Cause right, they find them like into one event rather than having a fact that thought that was interesting. Yeah. Yeah, cause usually it's one in the fall and one in the spring, I think. So anyway, now obviously, because it's not live, it's online, the cost was a little less. That was good to know. Yeah, but there's still about a $50 discount to register. So, and they always have a discount code that they provide and that you can input during the registration process to get your discount. So that's what's going on this year with them. And that's just coming up in a couple of weeks. So. Yep, it is. Yeah. You want to register. Yeah. This last slide just lists places you can go to stay informed. The most important thing I think is to make sure that someone at your library signed up for the trial mailing list. And I've got a URL there that you can go to that takes you to a page that has all the mailing lists maintained by the Nebraska Library Commission and it tells you how to sign up for the specific mailing lists. The trial mailing list. I don't think it really isn't that busy anymore. It used to be busier, but when we do have a new vendor approaching us and wanting to offer a trial and the discount, we'll send that information out. So it's a way to take advantage of database trials that are already set up. It's a way to express interest and lets you know when we're trying to see if we can get a group together for a particular database discount. So that's a good mailing list to be signed up for. As I said, the encompass blog we'll often post information to. And that also just shows up on the homepage of the Nebraska Library Commission website. The last three bullet points are just the specific pages for the three strands of the database program that I showed you earlier. And you know how to get there from the flyout menu on the left side of the Nebraska Library Commission website too. So hopefully you can use that and you won't have to type in the URLs. The last slide, I just want to mention the names of the people who work most closely with the program. Debra Dregos is the head of the technology access services department. And occasionally a vendor will contact her directly and will initiate a relationship by talking to her and saying we wanna work with you, we wanna offer a discount. And she may talk to them in initially and then at some point she'll pass them on to me and I'll work with them on getting details out and up on our website. And I'll work with them then on an ongoing basis. I guess I would say I'm in the primary contact if you have any questions about the program, you can contact me, I'm the one who sends out initial agreements to fill out if you're gonna subscribe to a database, I send out renewal agreements. Lots of times if I've worked with a vendor they just contact me directly when they wanna offer a discount or a promotion since they know I'm the one that they're ultimately gonna work with too. The other person that you may interact with at some point is Jennifer Rampey. She is the one that actually sends out invoices and she also helps me manage keeping track of renewals when they come in, especially at May, June when we have a whole bunch coming in it helps to have someone else kind of keeping track too. So Jennifer, if you have a question about can I be invoiced early? Have I been invoiced? Do you have a record of me having paid? Things like that. Jennifer would be the one to contact. Jennifer also can sometimes, if I'm out for some reason, Jennifer knows where I keep my paper files in the office and so sometimes she's been able to answer questions. She doesn't really, she's not really responsible for knowing the answer but she's been able to answer questions sometimes just because she knows where to dig around and find stuff when I'm out. And similarly, Jennifer is the one that does QuickBooks, sends out invoices, but I know enough to poke around and get in and I can usually see if you've been invoiced. I can resend invoices if for some reason you didn't receive it so I can answer those kinds of questions too. So when in doubt, call me but there are a couple other people that may also be able to help you as well. That kind of is a wrap from what I have planned so I don't know if anybody's had any questions, I'm more than happy to answer anything. Sure. Yeah, doesn't look anybody typed anything during while you're talking, that's okay. If anybody has any questions for Susan, go ahead and type them into your question section or let me know you wanna unmute your microphone and do it that way. Any questions about any of the services, any of the deals that she mentioned, or anyone's that maybe you're wondering if we have discounts on. And this is something that I love about this and I think I mentioned it last week when I was talking about this session we were having coming up. There's really no reason that you should ever pay full price for so many things that you do regularly at your library. Those lists as Susan was showing are huge of all the different companies and organizations or databases that we work in. This should be really, I think a library's first stop is what is the discount? Is it might already be available to me just because I'm in Nebraska from this company rather than just go directly to them, go and check these lists and see if there's something on there that I can benefit from. And there's so many things on there. There's, yeah, you shouldn't really be paying full price for anything. And I think it's also great, Susan, you mentioned, I was gonna mention earlier that a lot of this is a moving target when they're changing their prices or contacting us about new deals and having to negotiate. For many of our smaller libraries who don't have the staff to deal with that or the time to just go back and forth and back and forth with a vendor or a company on something and they just say, fine, I'll just pay it. Having you there to do it, I think is great that that's your job to spend all that time. Well, and it does help that I have, I know what they've charged other libraries that have come to us and so once in a while if they'll provide a price quote to a library and it seems way out of line, I can go back to them and say, hey, this library serves a similar pop served and you charge them this amount, what's the deal? And sometimes that'll make a difference. Other times it may be a situation where, well, these libraries were the initial group and they are grandfathered in at this special price. But once in a while, I've been, by doing that, they've sort of re-evaluated and brought the price back in line with the other libraries in the group. So having access to that information about what do other libraries that are comparably sized pay, I can sometimes will that information to our benefit too. Yeah, so you would argue. It's not information that I would just publicize and say, oh, here's what everybody pays for everything that's, I think, probably unethical and there are probably issues with doing that, but knowing that information and being able to, even without naming names sometimes indicate, well, that's quite a bit higher than another vendors. Any libraries question that too, I know we've had libraries contact us about lots of different services saying, or I would further talk about like, they're coding us this, is that a good, how do you even know? Is it a good price? Is it a, how is it comparable to other libraries? And sometimes our libraries are very collegial with each other and we'll maybe call the library down the road or the one they know is similar to them and say, hey, what do you guys get? Yeah. If you don't have that, even if you're just working directly to the library yourself, Susan can be, I think your resource for, can you let us know whatever other people might be getting so we can, if we do want to negotiate on our own, we're properly informed. Yeah, and I sometimes, and I don't have any, I don't feel like it's a problem for me to, if somebody's thinking about subscribing to something and maybe they want to try out, but maybe they want to talk to another library to see how it's worked in their library, to say, well, this library who's in your region subscribes to that product, so you might want to talk to them. It's not like it's completely private, that information's probably up on library's websites. It's just a matter of, it's more centralized. To find it might be, take more time than just giving a quick call to you and saying, hey, mom's already using this company, yeah. And again, that's part of our mission is trying to sort of coordinate and be sort of a central, central location for information and connect libraries to other libraries. So I feel like that's part of our mission. Absolutely, yeah. All right. Well, it doesn't look like we're a little after 11 o'clock. That's okay, we started a little after 10. It doesn't look like anybody has any desperate, urgent questions to ask you right now, and that's fine. I'm glad we got all those resources out there, all those great information out there. If you do have any questions, or any one thing you need to know about, give Susan a call, her information is there, you know where to find her anyways. Yeah, absolutely. Yeah, the recording will be available to you and the slides as well, Susan, you'll send me the slides. Yep. We'll get that up with the archive. All right, so I'm going to pull back, present your control to my screen again. It's up here, there we go. Yeah, so that will wrap it up for today's show. Thank you everyone for attending today. Thank you Susan for being here with us. The archive will be ready by the end of the week, as long as go to webinar and YouTube cooperate with me. Right here is, this is our main Encompass Live page. If you use search for Encompass Live, the name of our show on your search engine of choice. We're the only thing called that so far on the internet. Nobody else is allowed to use that name. And you'll find our homepage here of our upcoming shows, but then here is our archives list. So this is where the archive will go, and most recent one's the top of the list. So today's will be right here. You'll be able to click on it. This is the one from last week. There'll be a link to the recording and a link to the presentation that you'll be able to get to. While we're here, I'll show you, we do have a search feature here. You can search through all of our history of our shows if you wanted to find something on a particular topic. You can search the full archives or just most recent 12 months if you want to.  This is why we have a search feature now. Encompass Live premiered in January, 2009. So there are over 10 years worth of archives here. Every week we have a show. Once a month, once a year, we take off the week of our state, you know, conference usually, state library conference. But other than that, we've got a lot of shows here. So we do have a search feature. If you do go back farther, just pay attention to the original broadcast date of anything. Some things, because this information gets old, resources may have changed. Links might no longer work. Services and products may no longer exist sometimes. Things may need updating. So just pay attention when it was originally broadcast. Certain things will test, you know, the test of time will stand up to it, reading lists and things like that, of course, but certain things like Google Forms for 2017 probably has changed since then. But just pay attention when you are going through our archives or if you just want recent, just most recent years worth, just switch it to that before you search our archives. Encompass Live does also have a Facebook page. We've got links to that around here. Here's our Facebook page here where we post reminders. Here's a reminder to about today's show, letting people know when our recordings are ready, anything new that we're talking about on here. So anything about our show, you'll find here on our Facebook page. So if you do like to use Facebook, you can give us like there. You can also, we use other social media, Twitter, Instagram, I'm not sure what else. And we do have a hashtag for the show and come live. So if you want to search for that elsewhere as well, you will find information about our show. So that will wrap it up for today. In a couple of weeks, just want to remind you our library, our Nebraska libraries. I'm still working on getting some final information for next week's show, but two weeks from now, if you're looking for fund extra funding, library commission, we've got our grants coming out for 2021. We'll be talking about that on the 23rd. So if you're looking for information about getting grant funding from the commission on youth grants, internship grants and continuing education grants, watch that show, join us for that. I'll say, okay. So other than that, thank you everyone for being here. Hopefully we'll see you on an upcoming episode of Encompass Live. Bye-bye.


We've all heard the phrase, loose lips sink ships. To keep that from happening, follow the Operation Security Five Step process. So the five steps are identifying critical information. One of the first things that anybody should know is what information is important to them. The second step is identifying who the threat is or what the threat is. A particular adversary or it could be thieves in your neighborhood. The third step is taking a look at that critical information and who that threat is and understanding where you're vulnerable to that. The fourth step is identifying what type of risk you have associated with those particular things like your critical information. And the fifth step is applying measures or countermeasures to mitigate your particular risk. For more information about Operation Security, visit the Operation Security Facebook page.


I like to make fun of myself sometimes as well. Yeah, I'm going to get drunk on this soda water tonight. Watch me go. Or someone's like, let's drink. Let's get some shots and I'm like, yeah, no, I'm not drinking at the moment. I'm on soda water tonight. He's like, what are you talking about? Said, listen, I will go toe to toe with you on this alcohol. I will drink you under the table, my friend, with this soda water. Right? It's just something so lighthearted. Who cares? When the other person or the other group of people see that you don't care and that you're confident in choosing to be alcohol-free, they drop it. And even if they don't drop it and they keep coming at you, you just go, yeah, yeah, you're right. Yeah, haha. Yeah, I'm the non-drinker. It's not like, leave it alone. Just leave it alone, guys. It's like, yeah, yeah, yeah, I'm the non-drinker. I'm the crazy alcohol-free guy. I know. It's crazy. And just make fun of yourself. They will drop it. They will drop it because they will see your conviction and they're not like I'm white knuckling this.


What's up and welcome to One Take, I'm Gil and today I want to talk about the just announced John Wick spin-off film titled Ballerina. According to Deadline.com the movie Ballerina focuses on a young female assassin who seeks revenge against the people who killed her family. Now a few websites including Deadline.com are saying that we've actually seen this character. I don't know if that's exactly accurate. If you look at John Wick Chapter 3 there is a character in the film who is credited as Ballerina. But if you recall that was part of a whole group of Ballerinas that were being trained to be assassins. So I don't think it's clear that the one actress who was credited generically as Ballerina is the Ballerina. But I think it's a safe bet that the character in this movie will be part of that ballet troupe. Now I'm not automatically opposed to any sort of John Wick spin-off idea. In fact I'd say the world of John Wick is more ripe for spin-off than most movies because they've really built their own world here that functions by its own rules and they very clearly established that John Wick isn't the only interesting character in this world. However there are a few red flags for me around this Ballerina movie. First off the idea of a Ballerina assassin has kind of become a trope at this point. You have Black Widow from Marvel. There's the Red Sparrow movie with Jennifer Lawrence. So it feels a little bit like we've seen this concept before. On the other hand John Wick is a movie that's thrived on its visuals and a Ballerina assassin is certainly something that's ripe with opportunity for interesting visuals. Another red flag for me is how generic sounding the premise is. At least what we know so far a young female assassin seeks revenge against the people who killed her family. And you might say to me Gil look at the premise of John Wick. It was just about a guy seeking revenge because people killed his puppy. But that's part of what made the whole John Wick franchise so great. The fact that it takes this somewhat absurd premise takes it seriously but still has a sense of humor about it. I feel like all three John Wick films have done a great job of nailing that tone where it takes itself just seriously enough for you to get emotionally invested but it's still able to have pretty absurd plot elements like a lot of New York City's homeless secretly being assassins. So all three of these movies have had a serious enough tone but still a pretty strong sense of humor behind it. So obviously I'm reading a lot into really a fragment of a premise. But at least from that premise alone it makes me worried that they're not going to be able to capture that unique John Wick tone. Now to be honest I probably would give this movie more benefit of the doubt if not for the final red flag in all of this which is that they announced the director of this film will be Len Wiseman. He's best known for a few movies in the Underworld series and for Live Free or Die Hard. The fourth Die Hard film. I'm not totally familiar with the Underworld films and I actually thought Live Free or Die Hard was watchable. It was a totally fine movie but like I just talked about one of the things that's made the John Wick movies so successful is how they've managed to thread that needle and hit just the right tone between action drama and comedy. And unfortunately I just haven't really seen anything from this director that would give me the confidence that he can pull it off. Now it's always possible that Len Wiseman will surprise us and knock this one out of the park. There are a couple of things working in his favor. Number one, Shay Hayton. One of the writers from John Wick chapter three is returning to pen the script for Ballerina. Keanu Reeves is on as an executive producer. Now a lot of times executive producer doesn't mean a whole lot in terms of the creative direction of the film but Keanu Reeves gives me the impression that he's pretty protective of this franchise and really cares about it. So you'd hope that he'll at least be somewhat involved in the production of this film to make sure that it lives up to the John Wick brand. Anyway at this point we really know very little about this movie but as big a fan as I am of the John Wick franchise this news story worries me a little bit. It makes me wonder if they're going to keep expanding the John Wick franchise and risk tarnishing it or diluting it. So I'm definitely going into this one with some skepticism. Since we're talking about expansions of the John Wick franchise it's worth mentioning the other spin-off that was announced in the last couple of years. A TV show set to premiere on the stars network titled The Continental. This is another one that kind of worries me because one of the aspects of the John Wick franchise which is definitely enjoyable is the world building. I mentioned earlier the fact that much of New York City's homeless are truly secret assassins or the very concept of a hotel offering various services to assassins and sort of serving as a safe meeting ground for them. The hotel which is the show's namesake. All that stuff to me works well in the background of the John Wick films but I get the feeling that if you were to focus on those world building aspects and put them under a magnifying glass you'd start to see how sort of absurd all of it is. And I worry that a TV show called The Continental where you don't have John Wick at least not as a main character and you can't pull off the same sort of action stunts that you get in the film franchise at least not at the same caliber. You've got to assume they have more budgetary constraints on TV so when you lack all those elements and all of that world building and absurdity comes more to the forefront I worry that it could sort of fall apart a little bit. So I can't wait for John Wick chapter four which we know is coming but this ballerina spinoff the continental spinoff those are two things that I'm going into with a lot of skepticism but we don't know a lot about either of them at this point so I'll definitely wait and see and maybe a trailer will come out or something will be announced that gets me excited for one or both of these expansions of the John Wick franchise. Anyway I think that about wraps it up so if you enjoyed this video hit the like button subscribe to this channel and make sure to hit that little bell icon to make sure you get notifications whenever we release more videos like this one. Thanks for watching.


Casino State Labor Congress have joined their counterparts on a nationwide peaceful protest to drive home the demands from the federal government for total reversal of palm price and increment of minimum wage. The Labor Union, TUC and other affluent unions in the hundreds stage protest from NLC secretariat to Amado Bello stadium holding various inscriptions with chants saying good governance, not for hardship, stop import of petroleum products, build our refineries, stop anti-people policy among others. The State Chairman of the NLC, Comrade Suleimond Ayuba said that one day exercise is to cause the federal governments to order against its anti-people policy. Also, the trade union congress, a removal of fuel subsidy, increase in tuition fees have triple effect on over 200 million Nigerians. If we adjust this decision that was made on the podium, it's considered a lot of hardship. Can we be i.e.? No! As a general of the increase of tuition fees, university tuition fees, we want the government to look back to at least a considerable level of the price of cost of living generally. We also want an increase in the minimum wage of Nigeria because we don't have a living wage. We have a dead wage. We cannot live as a citizen to buy food, rents, medical bills, quite a number of things that will support us to live a living life in Nigeria. We hope that government will honor our demands to avoid further break of law and order or further process of maybe strike or whatever the decision may turn out to be for us. We are thinking that government will look inward and do the needful in elevating the sufferings not only of the workers but the Nigerian public as well.


Saturday, 9th of January. Still holiday hangover mode it looks like at the post offices. I'm a little tired this morning. I tried to stay awake to watch my alma mater, Michigan State basketball last night. I was up till 2. I watched till half time. We were up by 17 and what do you know? When I woke up this morning, looks like the other team came back and we lost by 1. Receiving packages in different countries when you don't speak the language fully. It was a challenge for me for a long time until I kind of figured out the system got everything down. Google translates a huge help. I've been waiting for these packages for a couple packages for more than two and a half weeks. And when I spend just ridiculous amounts of time looking on the internet following the packages tracking them knowing when I actually have to be home. And they were supposed to arrive yesterday but they didn't until I went outside late at night at 10pm and I saw this on my window. So I gotta go pick those wines up today and luckily they're open on Saturday morning but at first it was a beautiful morning but now it's snowing.  I'm just hoping there's not a super long line in the post office. So life has changed for a lot of us this year. Me as well. Instead of being able to travel full time with something I miss. When you're tasting wine at home you can taste it over a few hours or over a few days to see how the wines change. But this whole time showed me how much wine like a lot of other industries are built on connections with people. There's nothing like being there in the cellar, talking to some people that have the hands in the dirt, seeing the beautiful landscapes. That's what's drawn me to wine. That's what makes it magical for me. So I'm looking forward to 2021 hopefully returning somewhat to the norm. Line like expected. Yes! Do I have a dime? A tree packet. So two or three packages arrived I was expecting. The third one still two weeks later I haven't gotten. I got a good 25 kilos, about 55 pounds of wine to drag back. Luckily it's less than a kilometer away. Just taking a little break and now I suspect that delivery man just saw that it was on the sixth floor and maybe he didn't want to carry all the way up six floors even though there's a lift in our apartment. Actually I'm kind of glad there's only two of the boxes arrived because the third one arrived. I don't think that I'd be able to carry all of them and shoot this video. Woo doggy. So I got my workout in for the day. I think it was about 25, 30 kilos. So we're talking about 55, 60 pounds maybe even more over a kilometer. Left a little bit, a little more than a half mile. I think in crossfit terms they call that a farmer's carry or a fireman carry. Good thing I wasn't timed because I probably would have failed. So let's see what we got here. Mulit and Gurish Kaburla. This is a brand new producer for me. He reached out one and see if I could send a couple of wines. I think he sent a couple of vintages. Nice. One of my favorite producers in all of Slovenia on Belchnik was one of the guys that really started the amber wine, orange wine revolution over there. I had on the border of Colio, Italy along with Gravner and Radicon. Excellent. This is a producer to check out. So that's it. I hope you enjoyed watching me struggle carry some of those wines. And stay tuned to our YouTube channel for more exciting stuff. Check out our website, Exotic Wine Travel. I'll be doing a lot of articles on Slovenian wine. I'm tired. I'm going to rest. I will see you soon. Hello. Thanks for watching. Hey, you made it to the end. Make sure to subscribe to our YouTube channel. Click the bell so you know when new videos are out. If you like content like this, check out our Patreon page where you get some behind the scenes exclusive content. Thanks for watching. Cheers. Cheers.


This lecture is part of an online commutative algebra course and will be about irreducible subsets of the spectrum of a ring R. So you recall that if X is an element of any topological space, big X, then the closure of X is irreducible. Conversely, we show that in the spectrum of a ring R, any closed irreducible subset is of the form X bar for some X in the spectrum of R. So what this means is that we can classify all the closed irreducible subsets. In next lecture, we will see that for many rings, every closed set is a finite union of closed irreducible subsets. So this will classify all closed subsets of the spectrum of a ring. So let's give the proof of this. Suppose we have an irreducible closed subset. Now, any closed subset is of the form Z of i for some ideal i. So let Z of i be some irreducible closed subset. So here i is an ideal. And what we want to do is to show that Z of i is equal to the closure of p, where p is some ideal, prime ideal, considers a point of spectrum of R. So what's p going to be? Well, we could try taking p to be equal to i. The problem is i need not be prime, even if Z of i is irreducible. For example, i could be the ideal for in the integers and then Z of i, which is a single point and is irreducible. So we first of all have to fid with i a bit in order to make it into a prime ideal. And what we're going to do is we're going to replace i by its radical. So this is called the radical of i. So I'll just quickly recall what the radical of ideal is. So the radical of i is just the set of elements such that some power of the element is an i for n greater than or equal to one. And it's perhaps not immediately obvious that this is in fact an ideal. It's obviously closed under multiplication, but to see it's closed under addition, you have to think for a few seconds. So let's just take it's closed under addition. Well, if R and S are in the radical of i, we want to show that R plus S is in the radical of i. Well, we know R to the m is an i and S to the n is an i for some m and n. And now what about R plus S?  And now we see that all these bits here are divisible by S to the n, which is an i. Whereas all these bits here are divisible by R to the m, which is again an i. So all the terms in this are in i. So this is an element of i and this is indeed an ideal. So the radical of i is an ideal. Now we notice that if i is contained in an ideal p, then the radical of i is also contained in p because R to the n in p is equivalent to R being in p. So the prime ideals containing i are the same as the prime ideals containing the radical of i. So we may assume that i equals its own radical. So now we show that if i is the radical of i and z i is irreducible, then i is prime. And so pick a b with a times b in i. So we want to show that a is an i and b is an i because that's the definition of a prime ideal. So suppose not. Well, we have i a times i b is contained in i because a b is an i. So the prime ideals containing i a union, the prime ideals containing i b is equal to the set of prime ideals containing i. Now we notice this is irreducible by assumption and this is closed and this is closed. Now if an irreducible set is a union of two closed subsets, one of those subsets must be equal to for that set. So one of z i a, z i b, say z i a, is the same as z i. However, we're now going to get a contradiction from this because we notice that no power of a is in i because we assume that a was not in i and i is prime. So by the lemma below, which we're gonna prove shortly, there is a prime p disjoint from set one a, a squared and so on and containing i, but this contradicts z i a equals z i because we found a prime ideal p which is contained in that but p is not contained in that one there. So we've reached a contradiction from assuming that a and b are not in i, so we see that i is prime and now it's easier to check that z of i is just the closure of i where i is considered as a point of the spectrum. So that shows that our irreducible closed set z of i is in fact the closure of some point. Well, in the proof of that, we used a lemma that we postponed the proof of. So let's just state the lemma. Suppose s is a multiplicative subset of r. So just remember this means one in s and a in s, b in s implies a, b in s. And suppose it's a multiplicative subset disjoint from the ideal i, be any ideal of r. Then we can find a prime ideal p such that p is disjoint from s and p contains the ideal i. And proof of this is very easy. We pick p maximal among the ideals disjoint from s and containing i. So how do we do that? Well, whenever you're picking a maximal element of something, it's a pretty good guess you're using zon's lemma. So I'm just going to put the word zon here to show that p exists. So the set of ideals that are disjoint from s and contain i is not empty because it contains the ideal i. So by waving zon's lemma, this we see there is such a maximal ideal. And now we show p is prime. So suppose a, b is in p, then we want to show one of a or b is in p. Well, the ideals p plus a and p plus b cannot both contain elements of s because otherwise, because s is multiplicative, p would contain an element of s. So say p plus a is disjoint from s. By maximality of p, p is equal to p plus a because otherwise p plus a would be a bigger ideal that contained i and was disjoint from s. So a is in p. So we have shown that a, b is in p, implies a or b is in p, so p is prime. So that's the end of the proof of the lemma. By the way, this is fairly typical example of the fact that if you've got any set of ideals and you pick a maximal element of that set of ideals, then there's a pretty good chance that that maximal element is a prime ideal. So maximal elements of some set of ideals have a very strong tendency to be prime ideals. Anyway, so that completes the proof that any irreducible subset of spectrum of r is the closure of a point. For the rest of this lecture, I'm going to give another application of the useful lemma. This is a sort of slightly nasty example. The application is the spectrum of c of x is weird. So what is c of x? Well, here I'm going to be taking x to be compact house or space and c of x just means continuous functions, continuous real functions on x. So this is a ring under point-wise multiplication and we can ask what its spectrum is. Well, some bits of the spectrum are easy to figure out. So the maximal ideals of c of x are just the ideals mx for x in x where this is the functions vanishing. And as we saw earlier, you can in fact recover x from c of x by taking the maximal ideals to be the points of the space and then putting a suitable topology on it. And this is quite easy to see because if i is any ideal, suppose it's not contained in any of these maximal ideals. So such that for each x, we can find f of x in i with f of x none zero. Then we want to show that i is equal to the whole of the ring r. So let's write r for this ring. Well, that follows because we can cover x by the sets where f of x is not equal to zero. And these are open sets. So we can cover x by finite number of them because x is compact. So we've got a finite number. This produces a finite number of functions f of x such that x in x implies some f of x so for any y of x, some f of x is none zero at y. And now we just take the sum over this finite number of x of fx squared and we see that this is greater than zero at all points on x. So is a unit in i. So i is just equal to the whole ring. So the maximal ideals of c of x are very well behaved. They're just the points of x as you would probably guess. What about prime ideals? Well, this is where it gets a little bit stranger. First of all, every prime of c of x is contained in some, is contained in a unique maximal ideal mx for x in x. And that's very easy to see. If some ideal p is contained in mx and also contained in my, then we've got these points x, y in our space x and all we need to do is to pick a function that vanishes, that is none zero on x and another function, let's call this function g that is none zero on y. So we're taking f of x is none zero and g of y is none zero. And we also take fg to be the zero function. It's not too difficult to do that on a compact house or space. So we find fg is an i, so it is in p. So if p is prime, then it couldn't be contained in both mx and xy, so p is not prime. So every prime ideal is associated at some point. Next, it's quite easy to see that if p is closed and p is contained in mx, then p is not prime. It's not equal to mx. And this is quite easy to see because if y is not equal to x, p contains an element f with fy, none zero by primeness. So, and from this, you can easily check that p, that if p is closed, it's equal to m of x. I won't bother with the details since this is an algebra course, not an analysis course. However, and this is the point of this example, the none closed prime ideals can be weird. In fact, they're not only just can be weird, they are indeed weird. The problem is to show they exist. And if you try and construct one explicitly, you won't be able to. You can only show they exist sort of indirectly by using the lemma we had earlier. So what we're going to do is to pick a point x and we suppose that this is none isolated. And we're going to let i be the ideal of functions vanishing in the neighborhood of x. And we're going to pick the multiplicative subset s to be the powers of one f, f squared and so on, where fx is equal to zero, but f does not vanish in any neighborhood of x. And you can do this because x is not an isolated point. And then we see that by the lemma, we've got a multiplicative subset s disjoint from a. So we can find a prime p such that p is disjoint from s and p contains i. And the fact that p contains i, this implies that p is contained in the maximum ideal. Mx, because that's the only maximum ideal that can be contained in, but p is disjoint from s. And this implies that p is not equal to Mx because Mx contains this element f, but f is not an element of p. So we found none maximal and for that matter, none closed. Prime ideal. Well, except we haven't really found one because the proof of the lemma involves the axiom of choice. And it turns out that this is one of the cases when you can't really give an explicit construction of the ideal p without using some sort of, maybe some weak version of the axiom of choice. And the moral of this example is that if you're willing to use that topology when you mess around with ideals and you shouldn't even be thinking about none closed ideals because if you start working with none closed ideals, you get all these weird examples. And anyway, the whole point of an ideal is that you can quotient out by it and get a subring. And if you've got a none closed ideal and tried quotienting out by it, then you would get a none-house-dolphed ideal. And if you're using that topology when you mess around with ideals and you start out by it, then you would get a none-house-dolphed topology on the quotient, which is really extremely ugly.  Okay, so to summarize, this lecture we showed how to find the irreducible subsets of a ring. And next lecture, we're going to use that to classify all closed subsets of the spectrum of a notarian ring by showing that they're just unions, finite unions of irreducible closed subsets.