# 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 NakayamasLemma 2013-03-22 13:07:41 2013-03-22 13:07:41 n3o (216) n3o (216) 6 n3o (216) Theorem msc 13C99