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Let R {\displaystyle R} be a commutative unital ring and x 1 , x 2 , … , x n ∈ R {\displaystyle 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 , … , x n ) {\displaystyle K(x_{1},x_{2},\ldots ,x_{n})} , is defined as the Koszul complex of the element ( x 1 , x 2 , … , x n ) {\displaystyle (x_{1},x_{2},\ldots ,x_{n})} in the free R {\displaystyle R} -module R n {\displaystyle R^{n}} .
