abelian extension

Let K be a Galois extensionMathworldPlanetmath of F. The extensionPlanetmathPlanetmath is said to be an abelian extensionMathworldPlanetmathPlanetmath if the Galois groupMathworldPlanetmath Gal(K/F) is abelianMathworldPlanetmath.

Examples: (2)/ has Galois group /2 so (2)/ is an abelian extension.

Let ζn be a primitive nth root of unity (http://planetmath.org/RootOfUnity). Then (ζn)/ has Galois group (/n)* (the group of units of /n) so (ζn)/ is abelian.

Title abelian extension
Canonical name AbelianExtension
Date of creation 2013-03-22 13:09:28
Last modified on 2013-03-22 13:09:28
Owner scanez (1021)
Last modified by scanez (1021)
Numerical id 5
Author scanez (1021)
Entry type Definition
Classification msc 12F10
Related topic KroneckerWeberTheorem
Related topic KummerTheory