Lemma 15.45.11. Let $R$ be a Noetherian local ring. Then $R$ is a discrete valuation ring if and only if $R^ h$ is a discrete valuation ring if and only if $R^{sh}$ is a discrete valuation ring.
Lemma 15.45.11. Let $R$ be a Noetherian local ring. Then $R$ is a discrete valuation ring if and only if $R^ h$ is a discrete valuation ring if and only if $R^{sh}$ is a discrete valuation ring.
Proof. This follows from Lemmas 15.45.7 and 15.45.10 and Algebra, Lemma 10.119.7. $\square$
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