# Math Help - Non-trivial homomorphism

1. ## Non-trivial homomorphism

Let $f:R \rightarrow R$ a non-trivial ring homomorphism.

Prove:

a) $f(Q) \subset$ and $f|_Q = id_Q$
b) if $a > b$ then $f(a) > f(b)$
c) $f$ is smooth. Deduce that $f=id_R$

Thanks!

2. Maybe this helps?