Lemma 15.29.2. Let $R$ be a ring. Let $f_1, \ldots , f_ r \in R$. Let $M$ be an $R$-module. The extended alternating Čech complex of $M$ is the tensor product over $R$ of $M$ with the extended alternating Čech complex of $R$.

**Proof.**
Omitted.
$\square$

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