abelian number field

Definition 1.

An abelian number field is a number fieldMathworldPlanetmath K such that K/Q is an abelian extensionMathworldPlanetmathPlanetmath, i.e. K/Q is Galois and Gal(K/Q) is an abelian groupMathworldPlanetmath.

The abelian number fields are classified by the Kronecker-Weber TheoremMathworldPlanetmath.

Definition 2.

A cyclic number field is an (abelian) number field K such that K/Q is a Galois extensionMathworldPlanetmath and Gal(K/Q) is a finite cyclic groupMathworldPlanetmath (therefore abelian).

Title abelian number field
Canonical name AbelianNumberField
Date of creation 2013-03-22 16:01:24
Last modified on 2013-03-22 16:01:24
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 5
Author alozano (2414)
Entry type Definition
Classification msc 11-00
Related topic GaloisGroupsOfFiniteAbelianExtensionsOfMathbbQ
Defines cyclic number field