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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
• Talk:Algebraic number
  ...ging the statement "algebraic numbers can be complex" to the statement "an algebraic number is a complex number...", with the rationale that the second was correct and ...rs, but again, there is no canonical way to view this embedding. Thus, an algebraic number can generally be thought of as a complex number, but not in a canonical way
  7 KB (1,148 words) - 23:13, 10 December 2008
• Algebraic number/Approval
  12 bytes (1 word) - 10:54, 24 September 2007
• 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/Definition
  111 bytes (16 words) - 16:34, 13 July 2008
• Talk:Algebraic number field
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• 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 }}
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• Template:Algebraic number/Metadata
  | pagename = Algebraic number | abc = Algebraic number
  774 bytes (74 words) - 16:30, 13 July 2008
• 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
  4 KB (561 words) - 20:25, 5 December 2008
• Template:Algebraic number field/Metadata
  | pagename = algebraic number field | abc = algebraic number field
  2 KB (228 words) - 07:20, 15 March 2024
• Talk:Modulus (algebraic number theory)
  92 bytes (9 words) - 17:31, 27 October 2008
• Template:Modulus (algebraic number theory)/Metadata
  | pagename = Modulus (algebraic number theory) | abc = Modulus (algebraic number theory)
  2 KB (233 words) - 17:30, 27 October 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
• 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
• Talk:Discriminant of an algebraic number field
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• 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
• Template:Discriminant of an algebraic number field/Metadata
  | pagename = Discriminant of an algebraic number field | abc = Discriminant of an algebraic number field
  864 bytes (73 words) - 07:19, 15 March 2024
• 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
• User:Richard Pinch/Stubs
  * [[Discriminant of an algebraic number field]]
  352 bytes (43 words) - 04:36, 22 November 2023
• 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
  875 bytes (130 words) - 12:27, 8 May 2008
• 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
• 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}}
  715 bytes (91 words) - 17:34, 10 December 2008
• 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
• Template:Algebraic number/Metadata
  | pagename = Algebraic number | abc = Algebraic number
  774 bytes (74 words) - 16:30, 13 July 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
• Template:Discriminant of an algebraic number field/Metadata
  | pagename = Discriminant of an algebraic number field | abc = Discriminant of an algebraic number field
  864 bytes (73 words) - 07:19, 15 March 2024
• 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
• 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
• 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
• 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
  1 KB (152 words) - 08:31, 14 September 2013
• 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}}
  2 KB (206 words) - 19:38, 11 January 2010
• 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 }}
  151 bytes (17 words) - 02:37, 4 January 2013
• 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
• 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
• 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 }}
  865 bytes (110 words) - 02:29, 10 January 2013
• E (mathematics)/Related Articles
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  564 bytes (72 words) - 16:08, 11 January 2010
• Serge Lang/Related Articles
  {{r|Algebraic number field}} {{r|Algebraic number}}
  1 KB (187 words) - 20:18, 11 January 2010
• Algebraic number
  In [[mathematics]], and more specifically&mdash;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
• Algebra/Related Articles
  {{r|Algebraic number}}
  2 KB (247 words) - 06:00, 7 November 2010
• Number theory/Related Articles
  {{r|Algebraic number field}} {{r|Algebraic number}}
  2 KB (262 words) - 19:07, 11 January 2010
• Fermat's last theorem/Related Articles
  {{r|Algebraic number}}
  454 bytes (55 words) - 03:14, 21 October 2010
• Discriminant
  {{r|Discriminant of an algebraic number field}}
  136 bytes (19 words) - 11:05, 31 May 2009
• Golden ratio/Related Articles
  {{r|Algebraic number}}
  566 bytes (73 words) - 16:56, 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 ' * {{cite book | author=Pierre Samuel | authorlink=Pierre Samuel | title=Algebraic number theory | publisher=Hermann/Kershaw | year=1972 }}
  1 KB (172 words) - 15:42, 7 February 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_''L''/''K''. In a tower of fiel
  2 KB (382 words) - 09:40, 12 June 2009
• Minimal polynomial
  ...of a [[square matrix]], an [[endomorphism]] of a [[vector space]] or an [[algebraic number]]. ==Minimal polynomial of an algebraic number==
  4 KB (613 words) - 02:34, 4 January 2013
• 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
  4 KB (561 words) - 20:25, 5 December 2008
• Cyclotomic field/Related Articles
  {{r|Algebraic number field}}
  584 bytes (79 words) - 15:48, 11 January 2010
• Integral domain/Related Articles
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  675 bytes (89 words) - 17:28, 11 January 2010
• Quadratic field/Related Articles
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  644 bytes (86 words) - 19:50, 11 January 2010
• Template:Algebraic number field/Metadata
  | pagename = algebraic number field | abc = algebraic number field
  2 KB (228 words) - 07:20, 15 March 2024
• Talk:Algebraic number
  ...ging the statement "algebraic numbers can be complex" to the statement "an algebraic number is a complex number...", with the rationale that the second was correct and ...rs, but again, there is no canonical way to view this embedding. Thus, an algebraic number can generally be thought of as a complex number, but not in a canonical way
  7 KB (1,148 words) - 23:13, 10 December 2008
• Template:Modulus (algebraic number theory)/Metadata
  | pagename = Modulus (algebraic number theory) | abc = Modulus (algebraic number theory)
  2 KB (233 words) - 17:30, 27 October 2008
• User:Richard Pinch/Articles
  {{rpl|Algebraic number field}} {{rpl|Discriminant of an algebraic number field}}
  5 KB (628 words) - 04:35, 22 November 2023
• KANT/Related Articles
  {{r|Algebraic number field}}
  432 bytes (56 words) - 17:48, 11 January 2010
• Dedekind zeta function
  In [[mathematics]], to each [[algebraic number field]] ''k'', there is associated an important function called the '''Dede If ''k'' is an algebraic number field, the Dedekind zeta function of the field is a [[meromorphic function]
  2 KB (343 words) - 07:23, 1 January 2009
• 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
• Artin L-function/Related Articles
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  472 bytes (61 words) - 11:04, 11 January 2010
• Integral closure/Related Articles
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  497 bytes (63 words) - 17:28, 11 January 2010
• Monogenic field/Related Articles
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  476 bytes (61 words) - 18:38, 11 January 2010
• Cyclotomic field
  ...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=Pierre Samuel | authorlink=Pierre Samuel | title=Algebraic number theory | publisher=Hermann/Kershaw | year=1972 }}
  2 KB (342 words) - 12:52, 21 January 2009
• Order (ring theory)/Related Articles
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  502 bytes (64 words) - 19:15, 11 January 2010
• Minimal polynomial/Related Articles
  {{r|Algebraic number}}
  544 bytes (70 words) - 18:34, 11 January 2010
• Quadratic field
  ...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub ...art | authorlink=Ian Stewart (mathematician) | coauthors=D.O. Tall | title=Algebraic number theory | publisher=Chapman and Hall | year=1979 | isbn=0-412-13840-9 | page
  3 KB (453 words) - 17:18, 6 February 2009
• Ring (mathematics)/Related Articles
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  1 KB (174 words) - 20:03, 11 January 2010
• S-unit
  In [[mathematics]], in the field of [[algebraic number theory]], an '''''S'''''<nowiki></nowiki>'''-unit''' generalises the idea o *{{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=Springer | isbn=0-387-94225-4 | year=1986 }} Chap. V.
  3 KB (381 words) - 16:02, 28 October 2008
• Group homomorphism/Related Articles
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  762 bytes (99 words) - 17:00, 11 January 2010
• Rational number
  ...athbb{Q}</math>, i.e. the field of roots of rational polynomials, is the [[algebraic number]]s.
  9 KB (1,446 words) - 08:52, 30 May 2009
• Transcendental number/Related Articles
  {{r|Algebraic number}}
  850 bytes (136 words) - 15:22, 31 October 2008
• Different ideal/Related Articles
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  857 bytes (137 words) - 16:47, 30 October 2008
• Class field theory/Related Articles
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  924 bytes (147 words) - 17:24, 10 January 2013
• Integer
  The term '''rational integer''' is used in [[algebraic number theory]] to distinguish these "ordinary" integers, embedded in the [[field
  10 KB (1,566 words) - 08:34, 2 March 2024
• Field theory (mathematics)/Related Articles
  {{r|Algebraic number field}}
  1 KB (169 words) - 08:53, 22 December 2008
• Fermat's last theorem
  ...These include the [[unique factorization|unique factorization theorem]], [[algebraic number fields]], [[elliptic curves]], and [[modular form]]s.
  2 KB (340 words) - 12:36, 22 February 2012
• 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 a
  2 KB (315 words) - 15:49, 10 December 2008
• Module
  ...algebraic structures, such as algebraic topology, algebraic geometry, and algebraic number theory. A strong understanding of module theory is essential for anyone de
  7 KB (1,154 words) - 02:39, 16 May 2009
• Dedekind domain
  #Let <math>K</math> be an [[algebraic number field]]. Then the integral closure <math>o_K</math>of <math>\mathbb{Z}</mat
  2 KB (306 words) - 15:51, 10 December 2008
• Ring (mathematics)
  ...the study of [[polynomial|polynomial rings]] and [[Algebraic number field|algebraic number fields]] in the second half of the nineteenth century, amongst other by [[R
  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 el
  10 KB (1,637 words) - 16:03, 17 December 2008
• User talk:William Hart
  :::I have to admit I planned on adding some articles to algebraic number theory before treating things like elliptic curves and modular forms, so an ...ave been written might be difficult though. Anyhow, I want to have a go at algebraic number theory first. [[User:William Hart|William Hart]] 19:59, 23 February 2007 (C
  13 KB (2,289 words) - 08:03, 6 July 2007
• Real number
  ...[[rational number|rational]] or [[irrational number|irrational]]; either [[algebraic number|algebraic]] or [[transcendental number|transcendental]]; and either [[posit ...real numbers is [[uncountable|uncountably infinite]] but the set of all [[algebraic number]]s is [[countable|countably infinite]]. Contrary to widely held beliefs, hi
  19 KB (2,948 words) - 10:07, 28 February 2024
• Number theory
  ...odern subfields - in particular, [[analytic number theory|analytic]] and [[algebraic number theory]]. Algebraic number theory may be said to start with the study of reciprocity and cyclotomy, bu
  27 KB (4,383 words) - 08:05, 11 October 2011
• Number
  ...umber that is solution to a [[polynomial]] in integer coefficients is an [[algebraic number]]. This set includes all rational numbers and a subset of the irrational nu
  11 KB (1,701 words) - 20:07, 1 July 2021
• Prime number
  ...r, when one generalizes the concept of "integer", and starts considering [[algebraic number|algebraic integers]], it becomes clear that, while one can study elements t
  18 KB (2,917 words) - 10:27, 30 August 2014
• Talk:Number theory
  ...possibilities, such as outlining some of the main areas of number theory: algebraic number fields, zeta-functions and analytic methods, quadratic forms and lattices ( ...field in which such a statement would seem not to be approximately true is algebraic number theory: while the theory of ideals was motivated by an effort to make algeb
  30 KB (5,120 words) - 18:28, 1 January 2009
• Serge Lang
  ...ed ideas of his teacher, Artin; some of the most interesting passages in ''Algebraic Number Theory'' also reflect Artin's influence and ideas that might otherwise not
  7 KB (1,058 words) - 07:16, 9 June 2009
• User:Richard Pinch/References
  ...ink=J. W. S. Cassels | coauthors=[[Albrecht Fröhlich|A. Fröhlich]] | title=Algebraic Number Theory | publisher=[[Academic Press]] | year=1967 | isbn=012268950X }} ...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub
  26 KB (3,355 words) - 04:36, 22 November 2023
• Talk:Serge Lang
  ...considered a bias? You can certainly back it up by comparing "Algebra", "Algebraic Number Theory", and "Cyclotomic Fields I & II" with their competitors. (May I als
  3 KB (514 words) - 22:31, 30 March 2008
• CZ:Mathematics Workgroup
  *11Rxx [[Algebraic number theory]]: [[global field]]s {For [[complex multiplication]], see 11G15} *11Sxx Algebraic number theory: [[local field|local]] and <math>p</math>-adic fields
  24 KB (3,085 words) - 08:58, 23 March 2021
• Talk:Prime number/Draft
  ...ason is that with the development of algebraic number theory, the units in algebraic number fields were found to play a very special and important role. Within the in ...tart with the FToA point, etc, you could add your other points above about algebraic number theory, etc. [[User:J. Noel Chiappa|J. Noel Chiappa]] 00:38, 1 April 2008 (
  36 KB (6,274 words) - 16:22, 27 November 2008
• History of number theory
  ...ay, Gauss arguably made a first foray towards both [[Galois]]'s work and [[algebraic number theory]]. ...its rough subdivision into its current subfields - especially analytic and algebraic number theory - dates from that period.
  35 KB (5,526 words) - 11:29, 4 October 2013
• Talk:Complex number/Archive 1
  ...a bit of overkill. Of course, it's formally the same as the definition of algebraic number fields such as <math>\mathbb{Q}[\sqrt{-1}]</math> or <math>\mathbb{Q}[\sqrt ...tation. As Greg Woodhouse recalls to us, this notation is quite common for algebraic number theory specialists, to denote some quadratic fields. I still think it is a
  84 KB (14,397 words) - 17:02, 5 March 2024
• User:Subpagination Bot/Task 1/Log 1
  ...xander the Great]], [[Alfred J. Eggers]], [[Alfred Nobel]], [[Algebra]], [[Algebraic number]], [[Algebraic surface]], [[Algorithm]], [[Alistair Darling]], [[Allegheny
  18 KB (1,846 words) - 09:34, 16 April 2024
• User:Subpagination Bot/Bot test results/Log 1
  ...xander the Great]], [[Alfred J. Eggers]], [[Alfred Nobel]], [[Algebra]], [[Algebraic number]], [[Algebraic surface]], [[Algorithm]], [[Alistair Darling]], [[Allegheny
  18 KB (1,846 words) - 09:34, 16 April 2024
• Talk:Complex number/Draft
  ...other hand, number theory also uses complex numbers, e.g., when discussing algebraic number fields.
  62 KB (10,557 words) - 15:36, 2 October 2013