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.

Also see

 * Endomorphism Ring of Abelian Group is Ring with Unity: $\left({\operatorname {End} \left({G}\right), +, \circ}\right)$ is shown to be a ring.