\begin{definition}[Definition:R-Algebraic Structure Endomorphism]
Let $\struct {S, \ast_1, \ast_2, \ldots, \ast_n, \circ}_R$ be an $R$-algebraic structure.
Let $\phi: S \to S$ be an $R$-algebraic structure homomorphism from $S$ to itself.
Then $\phi$ is an $R$-algebraic structure endomorphism.
This definition continues to apply when $S$ is a module, and also when it is a vector space.
\end{definition}