Lemma 10.63.18. Let $R$ be a Noetherian local ring with maximal ideal $\mathfrak m$. Let $I \subset \mathfrak m$ be an ideal. Let $M$ be a finite $R$-module. The following are equivalent:

There exists an $x \in I$ which is not a zerodivisor on $M$.

We have $I \not\subset \mathfrak q$ for all $\mathfrak q \in \text{Ass}(M)$.

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