Field homomorphism

Let $F$ and $F'$ be fields. A function $\varphi:F \rightarrow F'$ is a field homomorphism if for all $a,b\in F$:

1. $\varphi(a+b)=\varphi(a)+\varphi(b)$
2. $\varphi(a\cdot b)=\varphi(a)\cdot\varphi(b)$
3. $\varphi(1)=1$

Remarks

• This is the same definition as a ring homomorphism, but between fields.