Corollary 2

Tag 0E2W, permanent. Cite it as [Bourbaki, Tag 0E2W].

Let $x=(x_1,\ldots,x_n)$ be a sequence of elements of $A$ , $M$ an $A$ -module, $x'$ the sequence $(x_1,\ldots,x_{n-1})$ . We have exact sequences

0\longrightarrow A/x_nA\otimes_A H_p(x',M)\longrightarrow H_p(x,M)\longrightarrow \operatorname{Hom}_A(A/x_nA,H_{p-1}(x',M))\longrightarrow 0.

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

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