\begin{definition}[Definition:Field Homomorphism]
Let $\struct {F, +, \times}$ and $\struct {K, \oplus, \otimes}$ be fields.
Let $\phi: F \to K$ be a mapping such that both $+$ and $\times$ have the morphism property under $\phi$.
That is, $\forall a, b \in F$:
{{begin-eqn}}
{{eqn | n = 1
      | l = \map \phi {a + b}
      | r = \map \phi a \oplus \map \phi b
}}
{{eqn | n = 2
      | l = \map \phi {a \times b}
      | r = \map \phi a \otimes \map \phi b
}}
{{end-eqn}}
Then $\phi: \struct {F, +, \times} \to \struct {K, \oplus, \otimes}$ is a field homomorphism.
\end{definition}