The Stacks project

Lemma 15.44.8. Given a Noetherian local ring $R$ we have $\text{depth}(R) = \text{depth}(R^ h) = \text{depth}(R^{sh})$.

Proof. By Lemma 15.44.3 we know that $R^ h$ and $R^{sh}$ are Noetherian. Hence the lemma follows from Algebra, Lemma 10.161.2. $\square$

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