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 $$R^n$$.