Galois module of roots of unity
= Galois module of roots of unity
{c}
{title2=$\mu_m\subseteq K_s^{\times}$}
The module $\mu_m$ consists of the $m$th roots of unity in a separable closure. If the field characteristic does not divide $m$, it has $m$ elements and fits into the Kummer sequence $1\to\mu_m\to K_s^{\times}\xrightarrow{m}K_s^{\times}\to1$. Its Galois action is the cyclotomic action; a generator gives a noncanonical identification with $\mathbb Z/m\mathbb Z$.