# Definition:Root of Unity/Primitive

## Definition

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:

$U_n = \set {1, \alpha, \ldots, \alpha^{n - 1} }$