Lemma 10.67.3. Let $R$ be a Noetherian ring. Let $M$ be a finite $R$-module. For any $f \in R$ we have $(M')_ f = (M_ f)'$ where $M \to M'$ and $M_ f \to (M_ f)'$ are the quotients constructed in Lemma 10.67.2.

Proof. Omitted. $\square$

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