Corollary 3

Tag 0E2X, permanent. Cite it as [Bourbaki, Tag 0E2X].

Algebra, chapter X, § 9. Complexes de Koszul

For $H_i(x,M)$ to be zero for all $i>0$ , it is necessary and sufficient that the homothety with ratio $x_n$ in $H_i(x',M)$ be bijective for $i>0$ , and that the homothety with ratio $x_n$ in $M/(x')M$ be injective.

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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