The Stacks project

Definition 10.32.1. Let $R$ be a ring. Let $I \subset R$ be an ideal. We say $I$ is locally nilpotent if for every $x \in I$ there exists an $n \in \mathbf{N}$ such that $x^ n = 0$. We say $I$ is nilpotent if there exists an $n \in \mathbf{N}$ such that $I^ n = 0$.