Koszul complex of a module

Definition
Let $$R$$ be a commutative unital ring and $$N$$ be a $$R$$-module. Let $$x \in N$$. Then the Koszul complex of $$x$$, denoted $$K(x)$$, is the complex of $$R$$-modules:

$$K(x): 0 \to R \to N \to \Lambda^2N \to \Lambda^3N \to \ldots $$

where the general map from $$\Lambda^iN$$ to $$\Lambda^{i+1}N$$ takes as input $$a$$ and outputs $$x \wedge a$$.

Related notions

 * Koszul complex of a sequence of elements