Definition:Endomorphism Ring of Abelian Group

Definition
Let $\struct {G, +}$ be an abelian group.

Let $\map {\mathrm {End} } G$ be the set of endomorphisms of $G$.

The endomorphism ring of $G$ is the algebraic structure:
 * $\struct {\map {\mathrm {End} } G, +, \circ}$

where:
 * $\circ$ denotes composition
 * $+$ denotes pointwise addition.

Also see

 * Endomorphism Ring of Abelian Group is Ring with Unity: $\struct {\map {\mathrm {End} } G, +, \circ}$ is shown to be a ring.