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• Algebraic number
  In [[mathematics]], and more specifically—in [[number theory]], an '''algebraic number''' is a [[complex number]] that is a root of a [[polynomial]] with [[ration ...s that ensued forms the foundation of modern [[algebraic number theory]]. Algebraic number theory is now an immense field, and one of current research, but so far has
  7 KB (1,145 words) - 00:49, 20 October 2013
• Algebraic number/Approval
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• Algebraic number/Definition
  111 bytes (16 words) - 16:34, 13 July 2008
• Algebraic number/Advanced
  ...x number]]s, but several recent authors have dropped this requirement. An algebraic number must be a root of a [[polynomial]] with [[rational number|rational]] coeffi ...s that ensued forms the foundation of modern [[algebraic number theory]]. Algebraic number theory is now an immense field, and one of current research, but so far has
  1 KB (179 words) - 14:14, 10 December 2008
• Algebraic number/Bibliography
  ...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub *{{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}
  2 KB (209 words) - 02:28, 22 December 2008
• Algebraic number field
  ...ory]], an '''algebraic number field''' is a principal object of study in [[algebraic number theory]]. The algebraic and arithmetic structure of a number field has app ...field]] '''Q''' of [[rational number]]s. The elements of ''K'' are thus [[algebraic number]]s. Let ''n'' = [''K'':'''Q'''] be the degree of the extension.
  7 KB (1,077 words) - 17:18, 10 January 2009
• Algebraic number field/Definition
  ...n of the rational numbers of finite degree; a principal object of study in algebraic number theory.
  151 bytes (22 words) - 03:01, 1 January 2009
• Algebraic number/Related Articles
  {{r|Algebraic number theory}} {{r|Algebraic number field}}
  887 bytes (126 words) - 02:29, 22 December 2008
• 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 extensio Let ''K'' be an algebraic number field with ring of integers ''R''. A ''modulus'' is a formal product
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• Algebraic number field/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Algebraic number field]]. Needs checking by a human. {{r|Algebraic number}}
  843 bytes (113 words) - 10:49, 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
  167 bytes (25 words) - 15:54, 5 December 2008
• Modulus (algebraic number theory)/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Modulus (algebraic number theory)]]. Needs checking by a human. {{r|Algebraic number field}}
  526 bytes (68 words) - 18:36, 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]
  1 KB (235 words) - 01:20, 18 February 2009
• Discriminant of an algebraic number field/Bibliography
  ...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub * {{cite book | author=Gerald Janusz | title=Algebraic Number Fields | publisher=Academic Press | year=1973 | isbn=0-12-380520-4 }}
  1 KB (153 words) - 14:18, 16 January 2013
• Discriminant of an algebraic number field/Definition
  An invariant attached to an extension of algebraic number fields which describes the geometric structure of the ring of integers and
  195 bytes (27 words) - 13:06, 23 December 2008
• 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

Page text matches

• Algebraic number/Advanced
  ...x number]]s, but several recent authors have dropped this requirement. An algebraic number must be a root of a [[polynomial]] with [[rational number|rational]] coeffi ...s that ensued forms the foundation of modern [[algebraic number theory]]. Algebraic number theory is now an immense field, and one of current research, but so far has
  1 KB (179 words) - 14:14, 10 December 2008
• 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
• Algebraic number field/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Algebraic number field]]. Needs checking by a human. {{r|Algebraic number}}
  843 bytes (113 words) - 10:49, 11 January 2010
• Dedekind zeta function/Related Articles
  {{r|Algebraic number theory}} {{r|Algebraic number field}}
  297 bytes (38 words) - 11:43, 15 June 2009
• Conductor of a number field
  ...field extension|extension]] of [[algebraic number field]]s is a [[modulus (algebraic number theory)|modulus]] which determines the splitting of [[prime ideal]]s. If n For a general extension ''F''/''K'', the conductor is a [[modulus (algebraic number theory)|modulus]] of ''K''.
  1 KB (177 words) - 01:07, 18 February 2009
• Order (ring theory)
  Any [[subring]] of an [[algebraic number field]] composed of [[algebraic integer]]s forms an order: the ring of all
  307 bytes (47 words) - 13:58, 1 February 2009
• Discriminant of an algebraic number field/Bibliography
  ...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub * {{cite book | author=Gerald Janusz | title=Algebraic Number Fields | publisher=Academic Press | year=1973 | isbn=0-12-380520-4 }}
  1 KB (153 words) - 14:18, 16 January 2013
• Different ideal/Bibliography
  * {{Citation | last=Weiss | first=Edwin | title=Algebraic number theory | publisher=Chelsea Publishing | year=1976 | isbn=0-8284-0293-0}}. ...ich | last2=Taylor | first2=Martin | authorlink2= Martin J. Taylor | title=Algebraic number theory | publisher=[[Cambridge University Press]] | series=Cambridge Studie
  470 bytes (55 words) - 09:40, 12 June 2009
• Transcendental number
  ...s]], a '''transcendental number''' is any [[complex number]] that is not [[algebraic number|algebraic]], i.e. it is not a root of any [[polynomial]] whose coefficients
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• 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]]
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• Algebraic number/Related Articles
  {{r|Algebraic number theory}} {{r|Algebraic number field}}
  887 bytes (126 words) - 02:29, 22 December 2008
• Field discriminant
  #REDIRECT [[Discriminant of an algebraic number field]]
  55 bytes (7 words) - 13:09, 23 December 2008
• Commutative algebra/Related Articles
  {{r|Algebraic number theory}}
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• Real number/Related Articles
  *[[Algebraic number]]
  389 bytes (39 words) - 12:37, 4 January 2009
• Ray class group
  #REDIRECT [[Modulus (algebraic number theory)#Ray class group]]
  63 bytes (8 words) - 06:18, 6 December 2008
• Dedekind zeta function/Definition
  Generalization of the Riemann zeta function to algebraic number fields.
  107 bytes (13 words) - 07:50, 22 September 2008
• KANT/Definition
  A computer algebra system for mathematicians interested in algebraic number theory.
  119 bytes (14 words) - 15:20, 28 October 2008
• Conductor of a number field/Definition
  Used in algebraic number theory; a modulus which determines the splitting of prime ideals.
  126 bytes (17 words) - 01:06, 18 February 2009
• 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
• 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
  167 bytes (25 words) - 15:54, 5 December 2008
• Modulus (algebraic number theory)/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Modulus (algebraic number theory)]]. Needs checking by a human. {{r|Algebraic number field}}
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• Rational number/Related Articles
  {{r|Algebraic number field}} {{r|Algebraic number}}
  1 KB (169 words) - 19:54, 11 January 2010
• Complex number/Related Articles
  {{r|Algebraic number}}
  276 bytes (34 words) - 10:41, 21 April 2010
• Conductor of a number field/Related Articles
  {{r|Algebraic number field}} {{r|Modulus (algebraic number theory)}}
  595 bytes (77 words) - 15:38, 11 January 2010
• Field (mathematics)/Related Articles
  {{r|Algebraic number field}} {{r|Algebraic number}}
  1 KB (146 words) - 16:32, 11 January 2010
• Class field theory/Definition
  <noinclude>{{Subpages}}</noinclude>The branch of algebraic number theory which studies the abelian extensions of a number field, or more gene
  171 bytes (26 words) - 17:18, 10 January 2013
• Different ideal/Definition
  An invariant attached to an extension of algebraic number fields which encodes ramification data.
  133 bytes (17 words) - 17:23, 20 November 2008
• 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
• KANT
  ...ted in algebraic number theory, performing sophisticated computations in [[algebraic number field]]s, in [[Global field|global]] [[function field]]s, and in [[local fi ...k | author=J. Graf von Schmettow | title=KANT — a tool for computations in algebraic number fields | booktitle=Computational number theory | publisher=de Gruyter | yea
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• 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
• Field extension/Related Articles
  {{r|Algebraic number field}} {{r|Discriminant of an algebraic number field}}
  857 bytes (112 words) - 16:32, 11 January 2010
• Polynomial/Related Articles
  {{r|Algebraic number}}
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• Algebraic number/Bibliography
  ...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub *{{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}
  2 KB (209 words) - 02:28, 22 December 2008
• Dedekind domain/Bibliography
  | title = Algebraic Number Theory
  240 bytes (22 words) - 07:44, 21 September 2008
• Root of unity/Related Articles
  {{r|Algebraic number field}} {{r|Algebraic number}}
  592 bytes (76 words) - 20:06, 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
• Genus field
  In [[algebraic number theory]], the '''genus field''' ''G'' of a [[number field]] ''K'' is the [[ * {{cite book | last=Ishida | first=Makoto | title=The genus fields of algebraic number fields | series=Lecture Notes in Mathematics | publisher=[[Springer Verlag]
  846 bytes (124 words) - 16:14, 28 October 2008
• Field extension
  ...lgebraic, but the converse need not hold. For example, the field of all [[algebraic number]]s over '''Q''' is an algebraic extension but not of finite degree.
  3 KB (435 words) - 22:38, 22 February 2009
• Minimal polynomial/Bibliography
  * {{cite book | author=Pierre Samuel | authorlink=Pierre Samuel | title=Algebraic number theory | publisher=Hermann/Kershaw | year=1972 }}
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• Modulus (disambiguation)
  {{r|Modulus (algebraic number theory)}}
  205 bytes (29 words) - 15:13, 10 January 2024
• Algebraic number field/Definition
  ...n of the rational numbers of finite degree; a principal object of study in algebraic number theory.
  151 bytes (22 words) - 03:01, 1 January 2009
• 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]
  1 KB (235 words) - 01:20, 18 February 2009
• Root of unity
  Roots of unity are clearly [[algebraic number]]s, and indeed [[algebraic integer]]s. It is often convenient to identify
  1 KB (197 words) - 22:01, 7 February 2009
• Discriminant of an algebraic number field/Definition
  An invariant attached to an extension of algebraic number fields which describes the geometric structure of the ring of integers and
  195 bytes (27 words) - 13:06, 23 December 2008
• Integer/Related Articles
  {{r|Algebraic number field}} {{r|Algebraic number}}
  2 KB (247 words) - 17:28, 11 January 2010
• 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 pol
  1 KB (208 words) - 16:47, 17 December 2008
• 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
• Conductor of a number field/Bibliography
  ...ink=J. W. S. Cassels | coauthors=[[Albrecht Fröhlich|A. Fröhlich]] | title=Algebraic Number Theory | publisher=[[Academic Press]] | year=1967 | isbn=012268950X }} * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}
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• Class field theory/Bibliography
  ...ink=J. W. S. Cassels | coauthors=[[Albrecht Fröhlich|A. Fröhlich]] | title=Algebraic Number Theory | publisher=[[Academic Press]] | year=1967 | isbn=012268950X }} * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}
  865 bytes (110 words) - 17:22, 10 January 2013