Definition:Z-Module Associated with Abelian Group/Definition 2

Definition
Let $\struct {G, *}$ be an abelian group with identity $e$.

Let $\struct {\Z, +, \times}$ be the ring of integers.

The $\Z$-module associated with $G$ is the $\Z$-module on $G$ with ring representation $\Z \to \map {\operatorname {End} } G$ equal to the initial homomorphism.

Also see

 * Equivalence of Definitions of Z-Module Associated with Abelian Group