\begin{definition}[Definition:Isomorphism (Abstract Algebra)/R-Algebraic Structure Isomorphism]
Let $\struct {S, \ast_1, \ast_2, \ldots, \ast_n, \circ}_R$ and $\struct {T, \odot_1, \odot_2, \ldots, \odot_n, \otimes}_R$ be $R$-algebraic structures.
Let $\phi: S \to T$ be an $R$-algebraic structure homomorphism.
Then $\phi$ is an $R$-algebraic structure isomorphism {{iff}} $\phi$ is a bijection.
\end{definition}