Lemma 1

Tag 0D0J, permanent. Cite it as [Bourbaki, Tag 0D0J].

Commutative Algebra, chapter X, § 1. Profondeur

If the $A$ -module $B$ is flat, the homomorphism $v^p$ is bijective for every integer $p$ .

This results from A, X, p. 66, Cor. 2.

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

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