I was reading Ring Homomorphism .
$\phi : R \to R'$ is a ring homomorphism and $e , e'$ are the unities of $R $ and $R'$ respectively.
I understood that $\phi (e) $ may not be unity of $R'$.
I think the following statements are true.
( 1 ) $\phi (e) $ is always unity of $\phi (R) $ .
(2) If $\phi $ is on to then $\phi (e) = e'$
(3) If $\phi $ is non trivial and $R'$ is a field then $\phi (e) = e'$.
Can someone check if there is any mistake in my understanding?
Yes your 3 statements are true and easy to prove ,I assume you can prove them .