\begin{definition}[Definition:Root of Unity/Primitive]
Let $n \in \Z_{> 0}$ be a strictly positive integer.
Let $F$ be a field.
A '''primitive $n$th root of unity of $F$''' is an element $\alpha \in U_n$ such that:
:$U_n = \set {1, \alpha, \ldots, \alpha^{n - 1} }$
\end{definition}