Definition:Endomorphism

An endomorphism is a homomorphism from an algebraic structure onto itself.

Group Endomorphism
If $$\left({S, \circ}\right)$$ is a group, then an endomorphism $$\phi: \left({S, \circ}\right) \to \left({S, \circ}\right)$$ is called a group endomorphism.

R-Algebraic Structure Endomorphism
If $$\left({S, \ast_1, \ast_2, \ldots, \ast_n: \circ}\right)_R$$ is an $R$-algebraic structure, then an endomorphism $$\phi: \left({S, \ast_1, \ast_2, \ldots, \ast_n: \circ}\right)_R \to \left({S, \ast_1, \ast_2, \ldots, \ast_n: \circ}\right)_R$$ is called an $$R$$-Algebraic Structure endomorphism.