Definition:Primitive Root of Unity/Definition 1

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:

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

Also see

• Equivalence of Definitions of Primitive Root of Unity

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): primitive ($n$-th root of unity)