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

Sources

• 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction ... (previous): $\S 3.4$ Hensel's Lemma
• 2007: Svetlana Katok: p-adic Analysis Compared with Real ... (previous): $\S 1.8$ Algebraic properties of $p$-adic integers