Definition:Field Homomorphism

Definition
Let $\left({F, +, \times}\right)$ and $\left({K, \oplus, \otimes}\right)$ be fields.

Let $\phi: F \to K$ be a mapping such that both $+$ and $\times$ have the morphism property under $\phi$.

That is, $\forall a, b \in F$:

Then $\phi: \left({F, +, \times}\right) \to \left({K, \oplus, \otimes}\right)$ is a field homomorphism.

Also see

 * Definition:Homomorphism (Abstract Algebra)
 * Definition:Ring Homomorphism


 * Definition:Field Epimorphism: a surjective field homomorphism


 * Definition:Field Monomorphism: an injective field homomorphism


 * Definition:Field Isomorphism: a bijective field homomorphism


 * Definition:Field Endomorphism: a field homomorphism from a field to itself


 * Definition:Field Automorphism: a field isomorphism from a field to itself