Example

Tag 00DP, permanent. Cite it as [Bourbaki, Tag 00DP].

Algebra, VIII, p. 200, § 11. Grothendieck Groups

If every finitely generated projective A-module is free, then the rank defines an isomorphism from $K_0(A)$ to $\mathbf{Z}$ . This is, in particular, the case when A is a principal ideal domain (VII, §1, No. 3, p. 15, Corollary 3) or when A is a local ring (VIII, p. 36, Corollary 6).

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

Nothing.

Cites

VIII, p. 36, Corollary 6