Corollary

Tag 051W, permanent. Cite it as [Bourbaki, Tag 051W].

Commutative Algebra, chapter VII, § 3. Factorial domains

If the completion of a Noetherian local ring $A$ is a factorial domain, $A$ is a factorial domain.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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