Definition:Root of Unity/Primitive

Definition
Let $n \in \Z_{> 0}$ be a strictly positive integer.

Let $F$ be a field.

A primitive $n^\text{th}$ root of unity of $F$ is an element $\alpha \in U_n$ such that:


 * $U_n = \left\{{1, \alpha, \ldots, \alpha^{n-1}}\right\}$