\begin{definition}[Definition:Isomorphism (Abstract Algebra)/F-Isomorphism]
Let $R, S$ be rings with unity.
Let $F$ be a subfield of both $R$ and $S$.
Let $\phi: R \to S$ be an $F$-homomorphism such that $\phi$ is bijective.
Then $\phi$ is an '''$F$-isomorphism'''.
The relationship between $R$ and $S$ is denoted $R \cong_F S$.
\end{definition}