Â The Ext functor of M and N can be computed by taking this type of resolution of N and then finding the Hom of the resolution and taking the homology of that complex, and this type of module can be defined by dualizing the commutative diagram that defines a projective module.
A module over R has this property if and only if every module homomorphism from an ideal of R to the module can be extended to a homomorphism from R to the module according to Baer's criterion. Â The Ext functor of M and N can be computed by taking this type of resolution of N and then finding the Hom of the resolution and taking the homology of that complex, and this type of module can be defined by dualizing the commutative diagram that defines a projective module. If a mapping into a space has a differential with this property, then that mapping is an immersion. (*) In a short exact sequence, A goes to B goes to C, the mapping on the left must have this property. This property is often checked by starting with f of a equals f of b and showing that in that case, a must equal b. The horizontal line test checks for this property and a bijection must be surjective and have this property. For ten points, name this property of mappings which means that each element of the domain is mapped to a unique element in the codomain.
A module over R has this property if and only if every module homomorphism from an ideal of R to the module can be extended to a homomorphism from R to the module according to Baer's criterion.
Injective [or one-to-one]