The question is:

Let m be a fixed positive int. For any integer a, let

$\displaystyle \bar{a}$ denote (a mod m) Show that the mapping of $\displaystyle \Phi: Z[x] \to Z_{m}[x]$ given by [Math]\Phi(a_nx^n + a_{n-1}x^{n-1}+...+a_0) = \bar{a_n}x^n + \bar{a_{n-1}}x^{n-1}+...+\bar{a_0}[/tex]

is a ring homomorphism.

All i want to know is that is it enough to show that $\displaystyle \phi : Z \to Z_m $ defined by $\displaystyle \phi(x) = $ x mod m is a homomorphism ?