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- 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
- 151 bytes (22 words) - 03:01, 1 January 2009
- 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''' is an invariant attached to an [[field extension|extension]] of [[algebraic number field]]s which describes the geometric structure of the [[ring of integers]] and1 KB (235 words) - 01:20, 18 February 2009
- 195 bytes (27 words) - 13:06, 23 December 2008
- 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
- ...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
- ...or''' or '''relative conductor''' of an [[field extension|extension]] of [[algebraic number field]]s is a [[modulus (algebraic number theory)|modulus]] which determines the1 KB (177 words) - 01:07, 18 February 2009
- 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
- {{r|Algebraic number field}} {{r|Discriminant of an algebraic number field}}857 bytes (112 words) - 16:32, 11 January 2010
- 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
- Any [[subring]] of an [[algebraic number field]] composed of [[algebraic integer]]s forms an order: the ring of all algebr307 bytes (47 words) - 13:58, 1 February 2009
- #REDIRECT [[Algebraic number field#Unit group]]47 bytes (6 words) - 05:12, 1 January 2009
- #REDIRECT [[Algebraic number field#Unit group]]47 bytes (6 words) - 05:06, 1 January 2009
- {{r|Algebraic number field}}595 bytes (77 words) - 15:38, 11 January 2010
- #REDIRECT [[Discriminant of an algebraic number field]]55 bytes (7 words) - 13:09, 23 December 2008
- {{r|Algebraic number field}}1 KB (146 words) - 16:32, 11 January 2010
- {{r|Algebraic number field}}1 KB (169 words) - 19:54, 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
- An algebraic number field generated over the rational numbers by roots of unity.116 bytes (16 words) - 13:28, 7 December 2008
- {{r|Algebraic number field}}297 bytes (38 words) - 11:43, 15 June 2009
- {{r|Algebraic number field}}887 bytes (126 words) - 02:29, 22 December 2008
- {{r|Algebraic number field}}592 bytes (76 words) - 20:06, 11 January 2010
- ...ted in algebraic number theory, performing sophisticated computations in [[algebraic number field]]s, in [[Global field|global]] [[function field]]s, and in [[local field]]s1 KB (152 words) - 08:31, 14 September 2013
- {{r|Algebraic number field}}526 bytes (68 words) - 18:36, 11 January 2010
- An algebraic number field for which the ring of integers is a polynomial ring.114 bytes (17 words) - 17:08, 28 October 2008
- 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 polynomia1 KB (208 words) - 16:47, 17 December 2008
- 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}}644 bytes (86 words) - 19:50, 11 January 2010
- ...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]] and1 KB (235 words) - 01:20, 18 February 2009
- {{r|Algebraic number field}}1 KB (187 words) - 20:18, 11 January 2010
- {{r|Algebraic number field}}584 bytes (79 words) - 15:48, 11 January 2010
- ...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
- {{r|Algebraic number field}}2 KB (247 words) - 17:28, 11 January 2010
- {{r|Discriminant of an algebraic number field}}136 bytes (19 words) - 11:05, 31 May 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 fields ''L2 KB (382 words) - 09:40, 12 June 2009
- {{r|Algebraic number field}}476 bytes (61 words) - 18:38, 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 ''K''.1 KB (172 words) - 15:42, 7 February 2009
- {{r|Algebraic number field}}1 KB (169 words) - 08:53, 22 December 2008
- 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]], def2 KB (343 words) - 07:23, 1 January 2009
- {{r|Algebraic number field}}2 KB (262 words) - 19:07, 11 January 2010
- {{r|Algebraic number field}}1 KB (174 words) - 20:03, 11 January 2010
- ...'''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 product4 KB (561 words) - 20:25, 5 December 2008
- {{r|Algebraic number field}}675 bytes (89 words) - 17:28, 11 January 2010
- {{r|Algebraic number field}}432 bytes (56 words) - 17:48, 11 January 2010
- {{r|Algebraic number field}}472 bytes (61 words) - 11:04, 11 January 2010
- 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
- {{r|Algebraic number field}}497 bytes (63 words) - 17:28, 11 January 2010
- {{r|Algebraic number field}}502 bytes (64 words) - 19:15, 11 January 2010
- #Let <math>K</math> be an [[algebraic number field]]. Then the integral closure <math>o_K</math>of <math>\mathbb{Z}</math> in2 KB (306 words) - 15:51, 10 December 2008
- {{r|Algebraic number field}}762 bytes (99 words) - 17:00, 11 January 2010
- ...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 jus2 KB (315 words) - 15:49, 10 December 2008
- ...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, amo10 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 elliptic10 KB (1,637 words) - 16:03, 17 December 2008
- ...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