Difference between revisions of "Abelian number field"
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| − | An Abelian extension of the field of rational numbers | + | An Abelian extension of the field of rational numbers $\mathbb{Q}$, i.e. a Galois extension $K$ of $\mathbb{Q}$ such that the Galois group $\mathrm{Gal}(K/\mathbb{Q})$ is Abelian. See [[Class field theory|Class field theory]]; [[Extension of a field|Extension of a field]]; [[Galois group|Galois group]]. |
Revision as of 20:58, 14 October 2014
An Abelian extension of the field of rational numbers $\mathbb{Q}$, i.e. a Galois extension $K$ of $\mathbb{Q}$ such that the Galois group $\mathrm{Gal}(K/\mathbb{Q})$ is Abelian. See Class field theory; Extension of a field; Galois group.
How to Cite This Entry:
Abelian number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Abelian_number_field&oldid=33666
Abelian number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Abelian_number_field&oldid=33666
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article