Definition:Isomorphism (Abstract Algebra)/Field Isomorphism

Definition
Let $\left({F, +, \circ}\right)$ and $\left({K, \oplus, *}\right)$ 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.