injective module

A module Q is an injective moduleMathworldPlanetmath if it satisfies the following equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath conditions:

(a) Every short exact sequenceMathworldPlanetmathPlanetmath of the form 0QBC0 is split (;

(b) The functorMathworldPlanetmath Hom(-,Q) is exact (;

(c) If f:XY is a monomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath and there exists a homomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath g:XQ, then there exists a homomorphism h:YQ such that hf=g.

Title injective module
Canonical name InjectiveModule
Date of creation 2013-03-22 12:02:26
Last modified on 2013-03-22 12:02:26
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 8
Author antizeus (11)
Entry type Definition
Classification msc 16D50