Karl Jones: Created page with "'''Algebraic number theory''' is a major branch of number theory that studies algebraic structures related to Algebraic integer|algebraic integer..."

2016-10-05T12:57:40Z

Created page with "'''Algebraic number theory''' is a major branch of number theory that studies algebraic structures related to Algebraic integer|algebraic integer..."

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'''Algebraic number theory''' is a major branch of [[number theory]] that studies [[Algebraic structure|algebraic structures]] related to [[Algebraic integer|algebraic integers]].

== Description ==

This is generally accomplished by considering a ring of algebraic integers O in an [[algebraic number field]] K/Q, and studying their algebraic properties such as [[factorization]], the behavior of [[Ideal (ring theory)|ideals]], and field extensions.

In this setting, the familiar features of the integers—such as [[unique factorization]]—need not hold. The virtue of the primary machinery employed—[[Galois theory]], [[group cohomology]], [[Group representation|group representations]], and [[L-function|L-functions]]—is that it allows one to deal with new phenomena and yet partially recover the behavior of the usual integers.

== See also ==

* [[Adele ring]]
* [[Arithmetic algebraic geometry]]
* [[Class field theory]]
* [[Ideal (ring theory)]]
* [[Ideal class group]]
* [[Iwasawa theory]]
* [[Kummer theory]]
* [[Langlands program]]
* [[Tamagawa number]]

== External links ==

* [https://en.wikipedia.org/wiki/Algebraic_number_theory Algebraic number theory] @ Wikipedia

[[Category:Mathematics]]

Algebraic number theory - Revision history

Karl Jones: Created page with "'''Algebraic number theory''' is a major branch of number theory that studies algebraic structures related to Algebraic integer|algebraic integer..."