Lemma 15.43.5. Let $A$ be a Noetherian local ring. Then $A$ is a discrete valuation ring if and only if $A^\wedge $ is so.
Lemma 15.43.5. Let $A$ be a Noetherian local ring. Then $A$ is a discrete valuation ring if and only if $A^\wedge $ is so.
Proof. This follows from Lemmas 15.43.1 and 15.43.4 and Algebra, Lemma 10.119.7. $\square$
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