\begin{definition}[Definition:Endomorphism Ring of Abelian Group]
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.
\end{definition}