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  • Class field theory
    ...theory]], '''class field theory''' studies the abelian extensions of an [[algebraic number field]], or more generally a [[global field]] or [[local field]].
    191 bytes (26 words) - 17:20, 10 January 2013
  • Conductor of a number field
    ...or''' or '''relative conductor''' of an [[field extension|extension]] of [[algebraic number field]]s is a [[modulus (algebraic number theory)|modulus]] which determines the
    1 KB (177 words) - 01:07, 18 February 2009
  • Algebraic number field/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Algebraic number field]]. Needs checking by a human. {{r|Discriminant of an algebraic number field}}
    843 bytes (113 words) - 10:49, 11 January 2010
  • Field extension/Related Articles
    {{r|Algebraic number field}} {{r|Discriminant of an algebraic number field}}
    857 bytes (112 words) - 16:32, 11 January 2010
  • Modulus (algebraic number theory)/Definition
    A formal product of places of an algebraic number field, used to encode ramification data for abelian extensions of a number field.
    167 bytes (25 words) - 15:54, 5 December 2008
  • Order (ring theory)
    Any [[subring]] of an [[algebraic number field]] composed of [[algebraic integer]]s forms an order: the ring of all algebr
    307 bytes (47 words) - 13:58, 1 February 2009
  • Dirichlet's unit theorem
    #REDIRECT [[Algebraic number field#Unit group]]
    47 bytes (6 words) - 05:06, 1 January 2009
  • Regulator of a number field
    #REDIRECT [[Algebraic number field#Unit group]]
    47 bytes (6 words) - 05:12, 1 January 2009
  • Conductor of a number field/Related Articles
    {{r|Algebraic number field}}
    595 bytes (77 words) - 15:38, 11 January 2010
  • Field discriminant
    #REDIRECT [[Discriminant of an algebraic number field]]
    55 bytes (7 words) - 13:09, 23 December 2008
  • Field (mathematics)/Related Articles
    {{r|Algebraic number field}}
    1 KB (146 words) - 16:32, 11 January 2010
  • Rational number/Related Articles
    {{r|Algebraic number field}}
    1 KB (169 words) - 19:54, 11 January 2010
  • Discriminant of an algebraic number field/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Discriminant of an algebraic number field]]. Needs checking by a human. {{r|Algebraic number field}}
    554 bytes (72 words) - 16:00, 11 January 2010
  • Cyclotomic field/Definition
    An algebraic number field generated over the rational numbers by roots of unity.
    116 bytes (16 words) - 13:28, 7 December 2008
  • Dedekind zeta function/Related Articles
    {{r|Algebraic number field}}
    297 bytes (38 words) - 11:43, 15 June 2009
  • Algebraic number/Related Articles
    {{r|Algebraic number field}}
    887 bytes (126 words) - 02:29, 22 December 2008
  • Root of unity/Related Articles
    {{r|Algebraic number field}}
    592 bytes (76 words) - 20:06, 11 January 2010
  • KANT
    ...ted in algebraic number theory, performing sophisticated computations in [[algebraic number field]]s, in [[Global field|global]] [[function field]]s, and in [[local field]]s
    1 KB (152 words) - 08:31, 14 September 2013
  • Modulus (algebraic number theory)/Related Articles
    {{r|Algebraic number field}}
    526 bytes (68 words) - 18:36, 11 January 2010
  • Monogenic field/Definition
    An algebraic number field for which the ring of integers is a polynomial ring.
    114 bytes (17 words) - 17:08, 28 October 2008
  • Monogenic field
    In [[mathematics]], a '''monogenic field''' is an [[algebraic number field]] for which there exists an element In a monogenic field ''K'', the [[Discriminant of an algebraic number field|field discriminant]] of ''K'' is equal to the [[discriminant of a polynomia
    1 KB (208 words) - 16:47, 17 December 2008
  • S-unit/Definition
    An element of an algebraic number field which has a denominator confined to primes in some fixed set.
    137 bytes (21 words) - 13:15, 5 December 2008
  • Quadratic field/Related Articles
    {{r|Algebraic number field}}
    644 bytes (86 words) - 19:50, 11 January 2010
  • Discriminant of an algebraic number field
    ...field''' is an invariant attached to an [[field extension|extension]] of [[algebraic number field]]s which describes the geometric structure of the [[ring of integers]] and
    1 KB (235 words) - 01:20, 18 February 2009
  • Serge Lang/Related Articles
    {{r|Algebraic number field}}
    1 KB (187 words) - 20:18, 11 January 2010
  • Cyclotomic field/Related Articles
    {{r|Algebraic number field}}
    584 bytes (79 words) - 15:48, 11 January 2010
  • Regulator of a number field/Definition
    ...c embedding of the generators of the unit group of the maximal order of an algebraic number field.
    168 bytes (25 words) - 05:11, 1 January 2009
  • Integer/Related Articles
    {{r|Algebraic number field}}
    2 KB (247 words) - 17:28, 11 January 2010
  • Discriminant
    {{r|Discriminant of an algebraic number field}}
    136 bytes (19 words) - 11:05, 31 May 2009
  • Different ideal
    ...], the '''different ideal''' is an invariant attached to an extension of [[algebraic number field]]s. ...tive norm]] of the relative different is equal to the [[Discriminant of an algebraic number field|relative discriminant]] Δ<sub>''L''/''K''</sub>. In a tower of fields ''L
    2 KB (382 words) - 09:40, 12 June 2009
  • Monogenic field/Related Articles
    {{r|Algebraic number field}}
    476 bytes (61 words) - 18:38, 11 January 2010
  • Integral closure
    ...e of integral closure is the [[ring of integers]] or maximal order in an [[algebraic number field]] ''K'', which may be defined as the integral closure of '''Z''' in ''K''.
    1 KB (172 words) - 15:42, 7 February 2009
  • Field theory (mathematics)/Related Articles
    {{r|Algebraic number field}}
    1 KB (169 words) - 08:53, 22 December 2008
  • Dedekind zeta function
    In [[mathematics]], to each [[algebraic number field]] ''k'', there is associated an important function called the '''Dedekind z If ''k'' is an algebraic number field, the Dedekind zeta function of the field is a [[meromorphic function]], def
    2 KB (343 words) - 07:23, 1 January 2009
  • Number theory/Related Articles
    {{r|Algebraic number field}}
    2 KB (262 words) - 19:07, 11 January 2010
  • Ring (mathematics)/Related Articles
    {{r|Algebraic number field}}
    1 KB (174 words) - 20:03, 11 January 2010
  • Modulus (algebraic number theory)
    ...'''cycle''') is a formal product of [[Place (mathematics)|place]]s of an [[algebraic number field]]. It is used to encode [[ramification]] data for [[abelian extension]]s o Let ''K'' be an algebraic number field with ring of integers ''R''. A ''modulus'' is a formal product
    4 KB (561 words) - 20:25, 5 December 2008
  • Integral domain/Related Articles
    {{r|Algebraic number field}}
    675 bytes (89 words) - 17:28, 11 January 2010
  • KANT/Related Articles
    {{r|Algebraic number field}}
    432 bytes (56 words) - 17:48, 11 January 2010
  • Artin L-function/Related Articles
    {{r|Algebraic number field}}
    472 bytes (61 words) - 11:04, 11 January 2010
  • Algebraic number field
    In [[number theory]], an '''algebraic number field''' is a principal object of study in [[algebraic number theory]]. The alge An ''algebraic number field'' ''K'' is a finite degree [[field extension]] of the [[field (mathematics)
    7 KB (1,077 words) - 17:18, 10 January 2009
  • Integral closure/Related Articles
    {{r|Algebraic number field}}
    497 bytes (63 words) - 17:28, 11 January 2010
  • Order (ring theory)/Related Articles
    {{r|Algebraic number field}}
    502 bytes (64 words) - 19:15, 11 January 2010
  • Dedekind domain
    #Let <math>K</math> be an [[algebraic number field]]. Then the integral closure <math>o_K</math>of <math>\mathbb{Z}</math> in
    2 KB (306 words) - 15:51, 10 December 2008
  • Group homomorphism/Related Articles
    {{r|Algebraic number field}}
    762 bytes (99 words) - 17:00, 11 January 2010
  • Artin L-function
    ...pace, there is an associated Artin L-function. When ''K'' and ''k'' are [[algebraic number field]]s, Artin L-functions generalize [[Dedekind zeta function]]s, which are jus
    2 KB (315 words) - 15:49, 10 December 2008
  • Ring (mathematics)
    ...f rings originated from the study of [[polynomial|polynomial rings]] and [[Algebraic number field|algebraic number fields]] in the second half of the nineteenth century, amo
    10 KB (1,667 words) - 13:47, 5 June 2011
  • Elliptic curve
    Let ''K'' be an [[algebraic number field]], a finite [[field extension|extension]] of '''Q''', and ''E'' an elliptic
    10 KB (1,637 words) - 16:03, 17 December 2008
  • Number theory
    ...y) is an algebraic number. Fields of algebraic numbers are also called ''[[algebraic number field]]s''.
    27 KB (4,383 words) - 08:05, 11 October 2011
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