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.

Sources

• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Algebraic Concepts