Remark (1)

Tag 0530, permanent. Cite it as [Bourbaki, Tag 0530].

Commutative Algebra, chapter VII, § 4. Modules over integrally closed Noetherian domains

Recall that for every sub-A-module M of V the canonical mapping $M \otimes_A K \to V$ is injective and has image KM (Algebra, Chapter II, § 7, no. 10, Proposition 26); to say that KM = V means therefore that this mapping is bijective.

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

Cited by

Nothing.

Cites

*Algebra*, Chapter II, § 7, no. 10, Proposition 26