Remarque 1

Tag 0E10, permanent. Cite it as [Bourbaki, Tag 0E10].

Algebra, chapter X, § 8. Dimension homologique

If $\mathrm{dh}(A) \leq n < +\infty$ , we have $\mathrm{Tor}_{n+1}^A(P, M) = 0$ for every $A$ -module $M$ and every right $A$ -module $P$ , since $\mathrm{dp}_A(M) \leq n$ (cf. lemma 1).

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

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