Nakayama’s lemma

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 $M=0$ .

Title	Nakayama’s lemma
Canonical name	NakayamasLemma
Date of creation	2013-03-22 13:07:41
Last modified on	2013-03-22 13:07:41
Owner	n3o (216)
Last modified by	n3o (216)
Numerical id	6
Author	n3o (216)
Entry type	Theorem
Classification	msc 13C99