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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 has7 KB (1,145 words) - 00:49, 20 October 2013
- ...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 way7 KB (1,148 words) - 23:13, 10 December 2008
- 111 bytes (16 words) - 16:34, 13 July 2008
- 12 bytes (1 word) - 17:17, 10 January 2009
- ...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
- | pagename = Algebraic number | abc = Algebraic number774 bytes (74 words) - 16:30, 13 July 2008
- 12 bytes (1 word) - 10:54, 24 September 2007
- ...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
- ...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
- | pagename = algebraic number field | abc = algebraic number field2 KB (228 words) - 07:20, 15 March 2024
- 92 bytes (9 words) - 17:31, 27 October 2008
- | pagename = Modulus (algebraic number theory) | abc = Modulus (algebraic number theory)2 KB (233 words) - 17:30, 27 October 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/Algebraic number field]]. Needs checking by a human. {{r|Algebraic number}}843 bytes (113 words) - 10:49, 11 January 2010
- 12 bytes (1 word) - 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
- ...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
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
- * [[Discriminant of an algebraic number field]]352 bytes (43 words) - 04:36, 22 November 2023
- ...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