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.

Title	cyclotomic extension
Canonical name	CyclotomicExtension
Date of creation	2013-03-22 15:05:17
Last modified on	2013-03-22 15:05:17
Owner	alozano (2414)
Last modified by	alozano (2414)
Numerical id	4
Author	alozano (2414)
Entry type	Definition
Classification	msc 11-00
Classification	msc 11R18
Related topic	KroneckerWeberTheorem
Related topic	CyclotomicField