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- 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
- Let us take the case that ''G'' is the [[Galois group]] of a [[field extension]] ''L''/''K''. A factor system in H<sup>2</sup>(''G'',''L''<sup>*</sup>) g3 KB (519 words) - 15:42, 2 January 2013
- An ''algebraic number field'' ''K'' is a finite degree [[field extension]] of the [[field (mathematics)|field]] '''Q''' of [[rational number]]s. Th7 KB (1,077 words) - 17:18, 10 January 2009
- ...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>\scriptsty5 KB (924 words) - 16:35, 11 December 2008
- * [[Algebraically independent set]]s in a [[field extension]];2 KB (334 words) - 16:29, 7 February 2009
- Let ''K'' be an [[algebraic number field]], a finite [[field extension|extension]] of '''Q''', and ''E'' an elliptic curve defined over ''K''. Th10 KB (1,637 words) - 16:03, 17 December 2008
- ...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
- ...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