Definition:Isomorphism (Abstract Algebra)/Field Isomorphism

Definition
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 $\phi$ is a bijection. That is, $\phi$ is a field isomorphism $\phi$ is both a monomorphism and an epimorphism.