In my textbook, it is said that
(Primitive root) Let $p$ be a prime and $n > 1$ be a natural number. The set of all the roots $\alpha$ of the polynomial $x^n - 1 \in Z_p[x]$ forms a cyclic group of order $n$, where all $\alpha$ belongs to the decomposition field of $x^n - 1$ over $Z_p$. If $a$ generates the prementioned group then we call $a$ to be the primitive root or order $n$ over $Z_p$.
I have no idea how to describe the decomposition field of that polynomial over $Z_p$. Please give me an insight to the problem. Thank you