\begin{definition}[Definition:Root of Unity/Order]
Let $n \in \Z_{> 0}$ be a strictly positive integer.
Let $F$ be a field.
Let $U_n = \set {z \in F: z^n = 1}$ be the $n$th roots of unity of $F$.
Let $z \in U_n$.
The '''order''' of $z$ is the smallest $p \in \Z_{> 0}$ such that:
:$z^p = 1$
Category:Definitions/Roots of Unity
\end{definition}