Proposition 5

Tag 0E14, permanent. Cite it as [Bourbaki, Tag 0E14].

Algebra, chapter X, § 8. Dimension homologique

Suppose $A$ is left noetherian and of finite homological dimension and let $\mathscr{C}_0$ (resp. $\mathscr{C}$ ) be the set of equivalence classes of finitely generated projective a-modules (resp. of a-modules). Then the canonical homomorphism of Grothendieck groups $K(\mathscr{C}_0) \to K(\mathscr{C})$ is bijective.

This follows from X, p. 137, Cor.

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

Cited by

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Cites

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