Koszul complex of a sequence of elements

Definition

Let $R$ be a commutative unital ring and $x_{1},x_{2},\ldots ,x_{n}\in R$ be a sequence of elements. The Koszul complex of this sequence, denoted $K(x_{1},x_{2},\ldots ,x_{n})$, is defined as the Koszul complex of the element $(x_{1},x_{2},\ldots ,x_{n})$ in the free $R$-module $R^{n}$.