# Definition:Endomorphism Ring of Abelian Group

## Definition

Let $\left({G, +}\right)$ be an abelian group.

Let $\operatorname{End} \left({G}\right)$ be the set of endomorphisms of $G$.

The endomorphism ring of $G$ is the algebraic structure:

$\left({\operatorname {End} \left({G}\right), +, \circ}\right)$

where:

$\circ$ denotes composition
$+$ denotes pointwise addition.