Search results
Jump to navigation
Jump to search
Page title matches
- 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 has7 KB (1,145 words) - 00:49, 20 October 2013
- ...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 has1 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
- ...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
- ...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 product4 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 number167 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 and195 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 has1 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 all307 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 Studie470 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 coefficients875 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
- Used in algebraic number theory; a modulus which determines the splitting of prime ideals.126 bytes (17 words) - 01:06, 18 February 2009
- An algebraic number field generated over the rational numbers by roots of unity.116 bytes (16 words) - 13:28, 7 December 2008
- A formal product of places of an algebraic number field, used to encode ramification data for abelian extensions of a number167 bytes (25 words) - 15:54, 5 December 2008
- 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
- {{r|Algebraic number field}} {{r|Algebraic number}}1 KB (169 words) - 19:54, 11 January 2010
- {{r|Algebraic number}}276 bytes (34 words) - 10:41, 21 April 2010
- {{r|Algebraic number field}} {{r|Modulus (algebraic number theory)}}595 bytes (77 words) - 15:38, 11 January 2010
- {{r|Algebraic number field}} {{r|Algebraic number}}1 KB (146 words) - 16:32, 11 January 2010
- <noinclude>{{Subpages}}</noinclude>The branch of algebraic number theory which studies the abelian extensions of a number field, or more gene171 bytes (26 words) - 17:18, 10 January 2013
- An algebraic number field for which the ring of integers is a polynomial ring.114 bytes (17 words) - 17:08, 28 October 2008
- An invariant attached to an extension of algebraic number fields which encodes ramification data.133 bytes (17 words) - 17:23, 20 November 2008
- ...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 | yea1 KB (152 words) - 08:31, 14 September 2013
- 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
- {{r|Algebraic number field}} {{r|Discriminant of an algebraic number field}}857 bytes (112 words) - 16:32, 11 January 2010
- {{r|Algebraic number}}2 KB (206 words) - 19:38, 11 January 2010
- ...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
- | title = Algebraic Number Theory240 bytes (22 words) - 07:44, 21 September 2008
- {{r|Algebraic number field}} {{r|Algebraic number}}592 bytes (76 words) - 20:06, 11 January 2010
- 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
- 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
- ...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
- * {{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
- {{r|Modulus (algebraic number theory)}}205 bytes (29 words) - 15:13, 10 January 2024
- ...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
- ...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
- Roots of unity are clearly [[algebraic number]]s, and indeed [[algebraic integer]]s. It is often convenient to identify1 KB (197 words) - 22:01, 7 February 2009
- An invariant attached to an extension of algebraic number fields which describes the geometric structure of the ring of integers and195 bytes (27 words) - 13:06, 23 December 2008
- {{r|Algebraic number field}} {{r|Algebraic number}}2 KB (247 words) - 17:28, 11 January 2010
- 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 pol1 KB (208 words) - 16:47, 17 December 2008
- ...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
- ...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
- ...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
- {{r|Algebraic number}}564 bytes (72 words) - 16:08, 11 January 2010
- {{r|Algebraic number field}} {{r|Algebraic number}}1 KB (187 words) - 20:18, 11 January 2010
- 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 has7 KB (1,145 words) - 00:49, 20 October 2013
- {{r|Algebraic number}}2 KB (247 words) - 06:00, 7 November 2010
- {{r|Algebraic number field}} {{r|Algebraic number}}2 KB (262 words) - 19:07, 11 January 2010
- {{r|Algebraic number}}454 bytes (55 words) - 03:14, 21 October 2010
- {{r|Discriminant of an algebraic number field}}136 bytes (19 words) - 11:05, 31 May 2009
- {{r|Algebraic number}}566 bytes (73 words) - 16:56, 11 January 2010
- ...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
- ...], 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 fiel2 KB (382 words) - 09:40, 12 June 2009
- ...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
- ...'''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 product4 KB (561 words) - 20:25, 5 December 2008
- {{r|Algebraic number field}}584 bytes (79 words) - 15:48, 11 January 2010
- {{r|Algebraic number field}}675 bytes (89 words) - 17:28, 11 January 2010
- {{r|Algebraic number field}}644 bytes (86 words) - 19:50, 11 January 2010
- {{r|Algebraic number field}}432 bytes (56 words) - 17:48, 11 January 2010
- 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
- ...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
- {{r|Algebraic number field}}472 bytes (61 words) - 11:04, 11 January 2010
- {{r|Algebraic number field}}497 bytes (63 words) - 17:28, 11 January 2010
- {{r|Algebraic number field}}476 bytes (61 words) - 18:38, 11 January 2010
- ...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
- {{r|Algebraic number field}}502 bytes (64 words) - 19:15, 11 January 2010
- {{r|Algebraic number}}544 bytes (70 words) - 18:34, 11 January 2010
- ...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 | page3 KB (453 words) - 17:18, 6 February 2009
- {{r|Algebraic number field}}1 KB (174 words) - 20:03, 11 January 2010
- 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
- {{r|Algebraic number field}}762 bytes (99 words) - 17:00, 11 January 2010
- ...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
- {{r|Algebraic number}}850 bytes (136 words) - 15:22, 31 October 2008
- {{r|Algebraic number theory}}857 bytes (137 words) - 16:47, 30 October 2008
- {{r|Algebraic number theory}}924 bytes (147 words) - 17:24, 10 January 2013
- The term '''rational integer''' is used in [[algebraic number theory]] to distinguish these "ordinary" integers, embedded in the [[field10 KB (1,566 words) - 08:34, 2 March 2024
- {{r|Algebraic number field}}1 KB (169 words) - 08:53, 22 December 2008
- ...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
- ...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 a2 KB (315 words) - 15:49, 10 December 2008
- ...algebraic structures, such as algebraic topology, algebraic geometry, and algebraic number theory. A strong understanding of module theory is essential for anyone de7 KB (1,154 words) - 02:39, 16 May 2009
- #Let <math>K</math> be an [[algebraic number field]]. Then the integral closure <math>o_K</math>of <math>\mathbb{Z}</mat2 KB (306 words) - 15:51, 10 December 2008
- ...the study of [[polynomial|polynomial rings]] and [[Algebraic number field|algebraic number fields]] in the second half of the nineteenth century, amongst other by [[R10 KB (1,667 words) - 13:47, 5 June 2011
- Let ''K'' be an [[algebraic number field]], a finite [[field extension|extension]] of '''Q''', and ''E'' an el10 KB (1,637 words) - 16:03, 17 December 2008
- ...[[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, hi19 KB (2,948 words) - 10:07, 28 February 2024
- ...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, bu27 KB (4,383 words) - 08:05, 11 October 2011
- ...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 nu11 KB (1,701 words) - 20:07, 1 July 2021
- ...r, when one generalizes the concept of "integer", and starts considering [[algebraic number|algebraic integers]], it becomes clear that, while one can study elements t18 KB (2,917 words) - 10:27, 30 August 2014
- ...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 not7 KB (1,058 words) - 07:16, 9 June 2009
- ...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