Corollary 4

Tag 005T, permanent. Cite it as [Bourbaki, Tag 005T].

Every finitely generated module over a principal ideal domain is balanced.

Indeed, a finitely generated module M over a principal ideal domain A is a generating $A_M$ -module (VIII, p. 81, Example 4).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Corollary 5, § 5

Cites

VIII, p. 81, Example 4