# module of finite rank

Let $M$ be a module, and let $E(M)$ be the injective hull of $M$. Then we say that $M$ has if $E(M)$ is a finite direct sum of indecomposable submodules.

This turns out to be equivalent to the property that $M$ has no infinite direct sums of nonzero submodules.

Title module of finite rank ModuleOfFiniteRank 2013-03-22 12:03:24 2013-03-22 12:03:24 antizeus (11) antizeus (11) 8 antizeus (11) Definition msc 16D80