Definition:Root of Unity/Primitive/Definition 2

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

Let $F$ be a field.

Let $U_n$ denote the set of all $n$-th roots of unity.

A primitive $n$th root of unity of $F$ is an element $\alpha \in U_n$ such that:
 * $\forall m : 0 < m < n : \alpha^m \ne 1$

Also see

 * Definition:Root of Unity/Primitive/Definition 1