Corollary
Tag 04BQ, permanent. Cite it as [Bourbaki, Tag 04BQ].
Commutative Algebra, chapter II, § 5. Finitely generated projective modules. Invertible fractional ideals
For a finitely generated projective A-module P to be of rank n, it is necessary and sufficient that be of rank 1.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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