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 sumMathworldPlanetmathPlanetmath of indecomposablePlanetmathPlanetmath submodules.

This turns out to be equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the property that M has no infiniteMathworldPlanetmath direct sums of nonzero submodules.

Title module of finite rank
Canonical name ModuleOfFiniteRank
Date of creation 2013-03-22 12:03:24
Last modified on 2013-03-22 12:03:24
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 8
Author antizeus (11)
Entry type Definition
Classification msc 16D80