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• Field extension
  In [[mathematics]], a '''field extension''' of a [[field (mathematics)|field]] ''F'' is a field ''E'' such that ''F' ...'E'' is a [[vector space]] over ''F''. The ''degree'' or ''index'' of the field extension [''E'':''F''] is the [[dimension]] of ''E'' as an ''F''-vector space. The
  3 KB (435 words) - 22:38, 22 February 2009
• Field extension/Definition
  83 bytes (12 words) - 13:18, 21 December 2008
• Field extension/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Field extension]]. Needs checking by a human.
  857 bytes (112 words) - 16:32, 11 January 2010

Page text matches

• Conductor of a number field
  ...c number theory]], the '''conductor''' or '''relative conductor''' of an [[field extension|extension]] of [[algebraic number field]]s is a [[modulus (algebraic number
  1 KB (177 words) - 01:07, 18 February 2009
• Separable extension
  #REDIRECT [[Field extension#Separable extension]]
  49 bytes (5 words) - 02:27, 20 December 2008
• Perfect field
  #REDIRECT [[Field extension#Separable extension]]
  49 bytes (5 words) - 02:30, 20 December 2008
• Simple extension
  #REDIRECT [[Field extension#Simple extension]]
  46 bytes (5 words) - 02:18, 20 December 2008
• Primitive element (field theory)
  #REDIRECT [[Field extension#Simple extension]]
  46 bytes (5 words) - 02:18, 20 December 2008
• Separable element
  #REDIRECT [[Field extension#Separable extension]]
  49 bytes (5 words) - 02:26, 20 December 2008
• Algebraic extension
  #REDIRECT [[Field extension#Algebraic extension]]
  49 bytes (5 words) - 11:53, 22 December 2008
• Normal extension
  ...gebra]], a '''normal extension''' of [[field (mathematics)|fields]] is a [[field extension]] ''E''/''F'' which contains all the roots of an irreducible polynomial if
  568 bytes (88 words) - 17:21, 7 February 2009
• Field extension
  In [[mathematics]], a '''field extension''' of a [[field (mathematics)|field]] ''F'' is a field ''E'' such that ''F' ...'E'' is a [[vector space]] over ''F''. The ''degree'' or ''index'' of the field extension [''E'':''F''] is the [[dimension]] of ''E'' as an ''F''-vector space. The
  3 KB (435 words) - 22:38, 22 February 2009
• Algebraic closure/Definition
  A field extension generated by the roots of all polynomials over the ground field.
  118 bytes (17 words) - 17:06, 6 January 2009
• Field extension/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Field extension]]. Needs checking by a human.
  857 bytes (112 words) - 16:32, 11 January 2010
• Extension field
  #REDIRECT [[Field extension]]
  29 bytes (3 words) - 04:13, 20 December 2008
• Normal extension/Related Articles
  {{r|Field extension}}
  530 bytes (68 words) - 19:04, 11 January 2010
• Separable extension/Definition
  A field extension in which all elements are separable.
  90 bytes (12 words) - 04:12, 20 December 2008
• Field (mathematics)/Related Articles
  {{r|Field extension}}
  1 KB (146 words) - 16:32, 11 January 2010
• Separable element/Definition
  An element of a field extension for which the minimal polynomial has distinct roots.
  120 bytes (17 words) - 04:11, 20 December 2008
• Normal extension/Definition
  A field extension which contains all the roots of an irreducible polynomial if it contains on
  141 bytes (21 words) - 13:16, 21 December 2008
• Quadratic field/Related Articles
  {{r|Field extension}}
  644 bytes (86 words) - 19:50, 11 January 2010
• Splitting field/Definition
  A field extension generated by the roots of a polynomial.
  93 bytes (13 words) - 13:13, 21 December 2008
• Artin-Schreier polynomial
  ...-Schreier polynomial''' is a polynomial whose roots are used to generate [[field extension]]s of [[prime number|prime]] degree ''p'' in [[characteristic of a field|ch
  2 KB (295 words) - 15:43, 7 December 2008
• Finite field/Related Articles
  {{r|Field extension}}
  692 bytes (91 words) - 16:33, 11 January 2010
• Cyclotomic field/Related Articles
  {{r|Field extension}}
  584 bytes (79 words) - 15:48, 11 January 2010
• Discriminant of an algebraic number field
  ...criminant of an algebraic number field''' is an invariant attached to an [[field extension|extension]] of [[algebraic number field]]s which describes the geometric st
  1 KB (235 words) - 01:20, 18 February 2009
• Algebraic number field/Definition
  A field extension of the rational numbers of finite degree; a principal object of study in al
  151 bytes (22 words) - 03:01, 1 January 2009
• Conductor of a number field/Related Articles
  {{r|Field extension}}
  595 bytes (77 words) - 15:38, 11 January 2010
• Discriminant of an algebraic number field/Related Articles
  {{r|Field extension}}
  554 bytes (72 words) - 16:00, 11 January 2010
• Different ideal
  ...s the [[ramification#In algebraic number theory|ramification]] data of the field extension ''L''/''K''. A prime ideal ''p'' of ''K'' ramifies in ''L'' if and only if
  2 KB (382 words) - 09:40, 12 June 2009
• Field theory (mathematics)/Related Articles
  {{r|Field extension}}
  1 KB (169 words) - 08:53, 22 December 2008
• Field automorphism
  ...bgroup <math>Aut_L(K)</math> of the full automorphism group of ''K''. A [[field extension]] <math>K/L</math> of finite index ''d'' is ''[[normal extension|normal]]''
  3 KB (418 words) - 12:18, 20 December 2008
• Minimal polynomial/Related Articles
  {{r|Field extension}}
  544 bytes (70 words) - 18:34, 11 January 2010
• Splitting field
  ..., a '''splitting field''' for a polynomial ''f'' over a field ''F'' is a [[field extension]] ''E''/''F'' with the properties that ''f'' splits completely over ''E'',
  1 KB (147 words) - 09:16, 4 July 2009
• Cyclotomic field
  ...''n''-th root of unity, then the ''n''-th cyclotomic field ''F'' is the [[field extension]] <math>\mathbf{Q}(\zeta)</math>.
  2 KB (342 words) - 12:52, 21 January 2009
• Quadratic field
  ...quadratic field''' is a [[Field theory (mathematics)|field]] which is an [[field extension|extension]] of its [[prime field]] of degree two.
  3 KB (453 words) - 17:18, 6 February 2009
• Rational function/Related Articles
  {{r|Field extension}}
  710 bytes (90 words) - 19:54, 11 January 2010
• Splitting field/Related Articles
  {{r|Field extension}}
  909 bytes (144 words) - 13:19, 21 December 2008
• Minimal polynomial
  ...The degree of the minimal polynomial of α is equal to the degree of the [[field extension]] '''Q'''(α)/'''Q'''. ...tisfies. The polynonmial ring ''F''[α] is then a field, and is the simple field extension ''F''(α). This field is a finite dimension al vector space over ''F'', on
  4 KB (613 words) - 02:34, 4 January 2013
• Galois theory
  Key concepts are [[Field extension|field extensions]] and [[Group theory|groups]], which should be thoroughly ...a subfield and also all the roots of ''f''. This field is known as the [[field extension|extension]] of ''K'' by the roots of ''f'', or the ''[[splitting field]]''
  4 KB (683 words) - 22:17, 7 February 2010
• Polynomial/Related Articles
  {{r|Field extension}}
  2 KB (206 words) - 19:38, 11 January 2010
• Matroid/Related Articles
  {{r|Field extension}}
  551 bytes (71 words) - 18:22, 11 January 2010
• Field (mathematics)
  *[[Field extension]]
  3 KB (496 words) - 22:16, 7 February 2010
• Quadratic equation/Advanced
  In Δ is not a square in ''F'' then the [[field extension]] <math>F(\sqrt\Delta)</math> is [[quadratic field|quadratic]] over ''F'':
  10 KB (1,580 words) - 08:52, 4 March 2009
• Factor system
  Let us take the case that ''G'' is the [[Galois group]] of a [[field extension]] ''L''/''K''. A factor system in H²(''G'',''L''^*) g
  3 KB (519 words) - 15:42, 2 January 2013
• Algebraic number field
  An ''algebraic number field'' ''K'' is a finite degree [[field extension]] of the [[field (mathematics)|field]] '''Q''' of [[rational number]]s. Th
  7 KB (1,077 words) - 17:18, 10 January 2009
• Fundamental Theorem of Algebra
  ...e one. Since <math>\scriptstyle\mathbb{C} = \mathbb{R}[i]</math>, any such field extension also extends <math>\scriptstyle\mathbb{R}</math>. Now, any <math>\scriptsty
  5 KB (924 words) - 16:35, 11 December 2008
• Matroid
  * [[Algebraically independent set]]s in a [[field extension]];
  2 KB (334 words) - 16:29, 7 February 2009
• Elliptic curve
  Let ''K'' be an [[algebraic number field]], a finite [[field extension|extension]] of '''Q''', and ''E'' an elliptic curve defined over ''K''. Th
  10 KB (1,637 words) - 16:03, 17 December 2008
• Complex number
  ...analysis, we could next show that <math>\mathbb{C}</math> has no finite [[field extension|extension]] and must therefore be [[algebraic closure|algebraically closed]
  18 KB (3,028 words) - 17:12, 25 August 2013
• Complex number/Citable Version
  ...analysis, we could next show that <math>\mathbb{C}</math> has no finite [[field extension|extension]] and must therefore be [[algebraic closure|algebraically closed]
  20 KB (3,304 words) - 17:11, 25 August 2013