\begin{definition}[Definition:F-Homomorphism]
Let $R, S$ be rings with unity.
Let $F$ be a subfield of both $R$ and $S$.
Then a ring homomorphism $\varphi: R \to S$ is called an '''$F$-homomorphism''' if:
:$\forall a \in F: \map \phi a = a$
That is, $\phi \restriction_F = I_F$ where:
:$\phi \restriction_F$ is the restriction of $\phi$ to $F$
:$I_F$ is the identity mapping on $F$.
\end{definition}