Definition:R-Algebraic Structure Automorphism

Definition
Let $\left({S, \ast_1, \ast_2, \ldots, \ast_n, \circ}\right)_R$ be an $R$-algebraic structure.

Let $\phi: S \to S$ be an $R$-algebraic structure isomorphism from $S$ to itself.

Then $\phi$ is an $R$-algebraic structure automorphism.

This definition continues to apply when $S$ is a module, and also when it is a vector space.