Endomorphism Ring of Abelian Group is Ring with Unity

Theorem

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

Let $\struct {\map {\mathrm {End} } G, +, \circ}$ be its endomorphism ring.

Then $\struct {\map {\mathrm {End} } G, +, \circ}$ is a ring with unity $I_G$, where $I_G$ is the identity mapping on $G$.

Proof

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Sources

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