NakayamasLemma 2002-11-03 10:36:24 2003-10-04 10:45:29 Theorem % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $R$ be a commutative ring with 1. Let $M$ be a finitely generated $R$-module. If there exists an ideal $\mathfrak{a}$ of $R$ contained in the Jacobson radical and such that $\mathfrak{a}M = M$, then $M=0$.