Lemma 15.45.8. Given a Noetherian local ring R we have \text{depth}(R) = \text{depth}(R^ h) = \text{depth}(R^{sh}).
Proof. By Lemma 15.45.3 we know that R^ h and R^{sh} are Noetherian. Hence the lemma follows from Algebra, Lemma 10.163.2. \square
Lemma 15.45.8. Given a Noetherian local ring R we have \text{depth}(R) = \text{depth}(R^ h) = \text{depth}(R^{sh}).
Proof. By Lemma 15.45.3 we know that R^ h and R^{sh} are Noetherian. Hence the lemma follows from Algebra, Lemma 10.163.2. \square
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