Ballieu showed that the number of these of order p cubed for p an odd prime is 3p + 50, two subtypes of these are shown to be equivalent by the Akizuki-Hopkins-Levitzski theorem. The number of strict inclusions in a maximal chain is used to define the Krull dimension of these objects, and Artinian ones don't contain a left or right chain of infinitely descending ideals. Modules are similar to vector spaces except that their coefficients come from one of these, and Guassian integers and Eisenstien integers both form one of these.  Those with a multiplicative identity and no zero divisors are known as integral domains. The one of the formal power series and number ones
Ballieu showed that the number of these of order p cubed for p an odd prime is 3p + 50, two subtypes of these are shown to be equivalent by the Akizuki-Hopkins-Levitzski theorem. The number of strict inclusions in a maximal chain is used to define the Krull dimension of these objects, and Artinian ones don't contain a left or right chain of infinitely descending ideals. Modules are similar to vector spaces except that their coefficients come from one of these, and Guassian integers and Eisenstien integers both form one of these.  Those with a multiplicative identity and no zero divisors are known as integral domains. The one of the formal power series and number ones are examples of Notherian ones, and they forms an Abelian group under addition, and a semigroup under multiplication. For 10 points, name this construct which is more general than a field.
Ballieu showed that the number of these of order p cubed for p an odd prime is 3p + 50, two subtypes of these are shown to be equivalent by the Akizuki-Hopkins-Levitzski theorem.
{Ring}