Physical Sciences and Mathematics Commons^™

Injective Modules And Divisible Groups, Ryan Neil Campbell

Masters Theses

An R-module M is injective provided that for every R-monomorphism g from R-modules A to B, any R-homomorphism f from A to M can be extended to an R-homomorphism h from B to M such that hg = [equals] f. That is one of several equivalent statements of injective modules that we will be discussing, including concepts dealing with ideals of rings, homomorphism modules, short exact sequences, and splitting sequences. A divisible group G is defined when for every element x of G and every nonzero integer n, there exists y in …