Lemma 10.60.6. Let $R$ be a Noetherian local ring. Then $\dim (R) = 0 \Leftrightarrow d(R) = 0$.

**Proof.**
This is because $d(R) = 0$ if and only if $R$ has finite length as an $R$-module. See Lemma 10.53.6.
$\square$

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