Proposition 19

Tag 0546, permanent. Cite it as [Bourbaki, Tag 0546].

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

Let $R$ be a finitely generated $B$ -module. For $R$ to be reflexive, it is necessary and sufficient that $R_{[A]}$ be a reflexive $A$ -module.

We have remarked in the proof of Proposition 18 that for R to be a torsion-free B-module, it is necessary and sufficient that $R_{[A]}$ be a torsion-free A-module. We may therefore assume that R is a lattice of $W = R \otimes_B L$ with respect to B. We shall use the following lemma:

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

Cited by

Lemma 4, § 4

Cites

Proposition 18