Definition 15.87.1. Let $R$ be a ring. Let $M$ be an $R$-module.

1. Let $I \subset R$ be an ideal. We say $M$ is an $I$-power torsion module if for every $m \in M$ there exists an $n > 0$ such that $I^ n m = 0$.

2. Let $f \in R$. We say $M$ is an $f$-power torsion module if for each $m \in M$, there exists an $n > 0$ such that $f^ n m = 0$.

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