Corollary 3

Tag 04GU, permanent. Cite it as [Bourbaki, Tag 04GU].

Commutative Algebra, chapter III, § 3. m-adic topologies on Noetherian rings

Let $A$ be a Zariski ring such that $\hat{A}$ is an integral domain and let $a$ be an ideal of $A$ . If the ideal $a\hat{A}$ of $\hat{A}$ is principal, $a$ is principal.

This is a special case of Corollary 2.

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

Cited by

Proposition 16, § 1

Cites

Corollary 2