Corollary

Tag 054I, permanent. Cite it as [Bourbaki, Tag 054I].

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

Let $M$ be a finitely generated $A$ -module and let $T$ be its torsion submodule. Then $T$ is a directfactor of $M$ .

As $M/T$ is torsion-free and finitely generated, it is projective by Proposition 22 and the corollary therefore follows from Algebra, Chapter II, § 2, no. 2, Proposition 4.

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

Cited by

Proposition 24, § 4

Cites

Proposition 22
Algebra, Chapter II, § 2, no. 2, Proposition 4