Koszul complex of a sequence of elements

Definition

Let $R$ be a commutative unital ring and $x_1,x_2,\dots ,x_n\in R$ be a sequence of elements. The Koszul complex of this sequence, denoted $K(x_1,x_2,\dots ,x_n)$, is defined as the Koszul complex of the element $(x_1,x_2,\dots ,x_n)$ in the free $R$-module $R^n$.