Graded Nakayama's lemma

This article is about the statement of a simple but indispensable lemma in commutative algebra
View other indispensable lemmata

Statement

Suppose $A$ is a graded ring. Let $A^{+}$ denote the ideal of all positively graded elements. Then, if $M$ is an $A$-graded module, $A^{+}M=M⟹M=0$.

Related results

• Nakayama's lemma