\begin{definition}[Definition:Isomorphism (Abstract Algebra)/Field Isomorphism]
Let $\struct {F, +, \circ}$ and $\struct {K, \oplus, *}$ be fields.
Let $\phi: F \to K$ be a (field) homomorphism.
Then $\phi$ is a field isomorphism {{iff}} $\phi$ is a bijection.
That is, $\phi$ is a field isomorphism {{iff}} $\phi$ is both a monomorphism and an epimorphism.
\end{definition}