Definition:F-Homomorphism

Definition

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:

$\forall a \in F: \varphi \left({a}\right) = a$.

That is, $\varphi \restriction_F = I_F$ where:

• $\varphi \restriction_F$ is the restriction of $\varphi$ to $F$
• $I_F$ is the identity mapping on $F$.

Also see

• $F$-Isomorphism