let $a$ a complex number , and $f$ be an irreducible polynomial with integer coefficients such that : $ f(a)=0$
1) Show that the set : $\{ g(a) \mid g \in \mathbf{Z}[X]\}$ is a ring isomorphic to $\mathbf{Z}^{n}$ respect to their group structure where $n=\deg f$
2) show that every non null Ideal of the previous ring is isomorphic to $\mathbf{Z}^{n}$ respect to their group sturcture
Help me to solve these questions with some hints please :)