# Injective

### Some articles on injective, injectives:

Injective Hull
... in the area of abstract algebra known as module theory, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest essential extension of it ... Injective hulls were first described in (Eckmann Schopf 1953), and are described in detail in the textbook (Lam 1999) ...
Resolution (algebra) - Resolutions in Abelian Categories
... The analogous notion of projective and injective modules are projective and injective objects, and, accordingly, projective and injective resolutions ... injective) resolution, then A is said to have enough projectives (resp ... enough injectives) ...
Injective Metric Space - Properties
... In an injective space, the radius of the minimum ball that contains any set S is equal to half the diameter of S ... Thus, injective spaces satisfy a particularly strong form of Jung's theorem ... Every injective space is a complete space (Aronszajn and Panitchpakdi 1956), and every metric map (or, equivalently, nonexpansive mapping, or short map) on a bounded injective ...
Algebraically Compact Group
... The group is pure injective, that is, injective with respect to exact sequences where the embedding is as a pure subgroup ... Every injective group is algebraically compact ...
Resolution (algebra) - Resolutions of Modules - Free, Projective, Injective, and Flat Resolutions
... Injective resolutions are right resolutions whose Ci are all injective modules ... Dually, every R-module possesses an injective resolution ... Analogously, the injective dimension id(M) and flat dimension fd(M) are defined for modules also ...