Definition 15.28.2. Let $R$ be a ring and let $f_1, \ldots , f_ r \in R$. The *Koszul complex on $f_1, \ldots , f_ r$* is the Koszul complex associated to the map $(f_1, \ldots , f_ r) : R^{\oplus r} \to R$. Notation $K_\bullet (f_\bullet )$, $K_\bullet (f_1, \ldots , f_ r)$, $K_\bullet (R, f_1, \ldots , f_ r)$, or $K_\bullet (R, f_\bullet )$.

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