Differential graded module

In algebra, a differential graded module, or dg-module, is a formula_1-graded module together with a differential; i.e., a square-zero graded endomorphism of the module of degree 1 or −1, depending on the convention. In other words, it is a chain complex having a structure of a module, while a differential graded algebra is a chain complex with a structure of an .
In view of the module-variant of Dold–Kan correspondence, the notion of an formula_2-graded dg-module is equivalent to that of a simplicial module; "equivalent" in the categorical sense; see below.
The Dold–Kan correspondence.
Given a commutative ring "R", by definition, the category of simplicial modules are simplicial objects in the category of modules over "R"; denoted by sMod"R". Then sMod"R" can be identified with the category of differential graded modules.