Proposition 15.86.5. Let $I \subset A$ be a finitely generated ideal of a ring $A$. Let $M$ be an $A$-module. The following are equivalent

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

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

Proposition 15.86.5. Let $I \subset A$ be a finitely generated ideal of a ring $A$. Let $M$ be an $A$-module. The following are equivalent

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

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

**Proof.**
This is clear from the results of Lemma 15.86.3.
$\square$

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