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  • 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
  • ...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
  • 12 bytes (1 word) - 10:54, 24 September 2007
  • 111 bytes (16 words) - 16:34, 13 July 2008
  • ...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
  • ...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
  • ...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
  • {{r|Algebraic number theory}} {{r|Algebraic number field}}
    887 bytes (126 words) - 02:29, 22 December 2008
  • ...'''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
    4 KB (561 words) - 20:25, 5 December 2008
  • 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
  • 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
  • ...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
  • 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
  • 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
  • ...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
  • 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

  • ...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
  • ...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
  • 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
  • {{r|Algebraic number theory}} {{r|Algebraic number field}}
    297 bytes (38 words) - 11:43, 15 June 2009
  • ...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
  • 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
  • ...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
  • * {{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
  • ...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
    875 bytes (130 words) - 12:27, 8 May 2008
  • #REDIRECT [[Algebraic number field#Unit group]]
    47 bytes (6 words) - 05:06, 1 January 2009
  • #REDIRECT [[Algebraic number field#Unit group]]
    47 bytes (6 words) - 05:12, 1 January 2009
  • {{r|Algebraic number theory}} {{r|Algebraic number field}}
    887 bytes (126 words) - 02:29, 22 December 2008
  • #REDIRECT [[Discriminant of an algebraic number field]]
    55 bytes (7 words) - 13:09, 23 December 2008
  • {{r|Algebraic number theory}}
    715 bytes (91 words) - 17:34, 10 December 2008
  • *[[Algebraic number]]
    389 bytes (39 words) - 12:37, 4 January 2009
  • #REDIRECT [[Modulus (algebraic number theory)#Ray class group]]
    63 bytes (8 words) - 06:18, 6 December 2008
  • Generalization of the Riemann zeta function to algebraic number fields.
    107 bytes (13 words) - 07:50, 22 September 2008
  • A computer algebra system for mathematicians interested in algebraic number theory.
    119 bytes (14 words) - 15:20, 28 October 2008
  • An algebraic number field generated over the rational numbers by roots of unity.
    116 bytes (16 words) - 13:28, 7 December 2008
  • Used in algebraic number theory; a modulus which determines the splitting of prime ideals.
    126 bytes (17 words) - 01:06, 18 February 2009
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