The Stacks project

Lemma 42.68.32. Let $A$ be a Noetherian local ring and $M$ a finite $A$-module of dimension $1$. Let $a \in A$ be a nonzerodivisor on $M$. Then $d_ M(a, a) = (-1)^{\text{length}_ A(M/aM)}$.

Proof. Immediate from Lemma 42.68.16. $\square$

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