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• Splitting field
  In [[algebra]], a '''splitting field''' for a polynomial ''f'' over a field ''F'' is a [[field extension]] ''E'' A splitting field for a given polynomial always exists, and is unique up to [[field isomorphi
  1 KB (147 words) - 09:16, 4 July 2009
• Splitting field/Definition
  93 bytes (13 words) - 13:13, 21 December 2008
• Splitting field/Related Articles
  909 bytes (144 words) - 13:19, 21 December 2008

Page text matches

• Field extension/Related Articles
  {{r|Splitting field}}
  857 bytes (112 words) - 16:32, 11 January 2010
• Splitting field
  In [[algebra]], a '''splitting field''' for a polynomial ''f'' over a field ''F'' is a [[field extension]] ''E'' A splitting field for a given polynomial always exists, and is unique up to [[field isomorphi
  1 KB (147 words) - 09:16, 4 July 2009
• Normal extension/Related Articles
  {{r|Splitting field}}
  530 bytes (68 words) - 19:04, 11 January 2010
• Cyclotomic field
  ...Since the powers of ζ are the roots of the latter polynomial, ''F'' is a [[splitting field]] for <math>\Phi_n(X)</math> and hence a [[Galois extension]]. The [[Galoi
  2 KB (342 words) - 12:52, 21 January 2009
• Quadratic field
  ...of <math>X^2 - d</math> and both roots lie in the field, which is thus a [[splitting field]] and so a [[Galois extension]]. The [[Galois group]] is cyclic of order t
  3 KB (453 words) - 17:18, 6 February 2009
• Serge Lang/Related Articles
  {{r|Splitting field}}
  1 KB (187 words) - 20:18, 11 January 2010
• Galois theory/Related Articles
  {{r|Splitting field}}
  990 bytes (154 words) - 13:18, 20 December 2008
• Finite field
  ...math>\mathbb{F}_p</math>, let <math>f(x) := x^{p^n}-x</math>. Let F be the splitting field of f over <math>\mathbb{F}_p</math>.
  2 KB (406 words) - 20:45, 8 February 2010
• Artin-Schreier polynomial
  ...fore, both roots of the equation lie in the extension, which is thus a ''[[splitting field]]'' for the equation and hence a [[Galois extension]]: in this case the roo
  2 KB (295 words) - 15:43, 7 December 2008
• Polynomial/Related Articles
  {{r|Splitting field}}
  2 KB (206 words) - 19:38, 11 January 2010
• Algebra/Related Articles
  {{r|Splitting field}}
  2 KB (247 words) - 06:00, 7 November 2010
• Galois theory
  ...e [[field extension|extension]] of ''K'' by the roots of ''f'', or the ''[[splitting field]]'' of ''f'' over ''K''. It is unique up to isomorphism..
  4 KB (683 words) - 22:17, 7 February 2010
• Quadratic equation/Advanced
  ...'F'': both roots of the equation lie in the extension, which is thus a ''[[splitting field]]'' for the equation and hence a [[Galois extension]]. ...fore, both roots of the equation lie in the extension, which is thus a ''[[splitting field]]'' for the equation and hence a [[Galois extension]]: in this case the roo
  10 KB (1,580 words) - 08:52, 4 March 2009
• Fundamental Theorem of Algebra
  ...mial must have a real root by the [[intermediate value theorem]], so the [[splitting field]] of <math>\scriptstyle\alpha</math> over <math>\mathbb{R}</math> must have
  5 KB (924 words) - 16:35, 11 December 2008