injective module

A module $Q$ is an injective moduleif it satisfies the following equivalent conditions:

(a) Every short exact sequenceof the form $0\to Q\to B\to C\to 0$is split (http://planetmath.org/SplitShortExactSequence);

(b) The functor $\mathrm{Hom}(-,Q)$is exact (http://planetmath.org/ExactFunctor);

(c) If $f:X\to Y$ is a monomorphismand there exists a homomorphism $g:X\to Q$,then there exists a homomorphism $h:Y\to Q$such that $hf=g$.