Definition:Isomorphism (Abstract Algebra)/F-Isomorphism

Definition
Let $R, S$ be rings with unity.

Let $F$ be a subfield of both $R$ and $S$.

Let $\varphi: R \to S$ be an $F$-homomorphism such that $\varphi$ is bijective.

Then $\varphi$ is an $F$-isomorphism.

The relationship between $R$ and $S$ is denoted $R \ \cong_F \ S$.

Also see

 * $F$-Isomorphism