cyclotomic extension

Definition.

Let $K$ be a field and let $\overline{K}$ be a fixed algebraic closure of $K$. A cyclotomic extension of $K$ is an extension field of the form $K\mathit{}\mathrm{(}\zeta \mathrm{)}$ where $\zeta \mathrm{\in }\overline{K}$ is a root of unity.