Let M be a left (or right) R-module. The socle of M, denoted by Soc(M), is the sum of all simple (or minimal) submodules of M. If M has no simple submodules, then Soc(M):=(0).

A left (or right) R-module M is semisimplePlanetmathPlanetmathPlanetmathPlanetmath iff Soc(M)=M.

Title socle
Canonical name Socle
Date of creation 2013-03-22 14:21:26
Last modified on 2013-03-22 14:21:26
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 5
Author CWoo (3771)
Entry type Definition
Classification msc 16D99
Related topic SemisimpleGroup