Proposition 15.91.5. Let $I \subset A$ be a finitely generated ideal of a ring $A$. Let $M$ be an $A$-module. The following are equivalent

1. $M$ is $I$-adically complete, and

2. $M$ is derived complete with respect to $I$ and $\bigcap I^ nM = 0$.

Proof. This is clear from the results of Lemma 15.91.3. $\square$

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