Definition:Isomorphism (Abstract Algebra)/F-Isomorphism
Let $R, S$ be rings with unity.
Let $F$ be a subfield of both $R$ and $S$.
Then $\phi$ is an $F$-isomorphism.
The relationship between $R$ and $S$ is denoted $R \cong_F S$.
The word isomorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.
Thus isomorphism means equal structure.