simple moduleSimpleModule2001-11-24 02:02:582005-09-26 14:25:04Definition\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}Let $R$ be a ring, and let $M$ be an $R$-module.
We say that $M$ is a {\PMlinkescapetext {\it simple}}
or {\PMlinkescapetext {\it irreducible}} {\PMlinkescapetext module }
if it contains no submodules
other than itself and the zero module.
Typically, by convention, the zero module is not itself considered simple.