Corollary 1

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

Let $A$ be a Zariski ring, $E$ a finitely generated $A$ -module and $F$ a submodule of $E$ . Then $F = \hat{F} \cap E = (\hat{A}F) \cap E$ .

This is a special case of Chapter I, § 3, no. 5, Proposition 10 (ii) and it also follows from no. 3, Proposition 6.

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

Cited by

Nothing.