Prove that if F is a field, R is a ring, and $\displaystyle \theta :F\rightarrow R$ is a ring homomorphism, then either$\displaystyle \theta$ is one to one or $\displaystyle \theta(a)=0$ for all a in F.
i'm stuck on this proof.
Thank you.
Prove that if F is a field, R is a ring, and $\displaystyle \theta :F\rightarrow R$ is a ring homomorphism, then either$\displaystyle \theta$ is one to one or $\displaystyle \theta(a)=0$ for all a in F.
i'm stuck on this proof.
Thank you.