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- Now suppose that <math>n > 0</math>. Let <math>C</math> be a [[splitting field]] of <math>F</math> over <math>\mathbb{C}</math>, and let <math>x_1, \dotsc5 KB (832 words) - 13:22, 11 January 2024
- ...[[splitting field]] of the polynomial <math>x^q - 1</math> over the finite field <math>\mathbb{F}_p</math>. Let <math>\zeta</math> be a primitive <math>q</ ''Proof.'' Let <math>K</math> be the splitting field of the polynomial7 KB (1,182 words) - 15:46, 28 April 2016
- ...^2,\ldots,\zeta_n^{n-1}</math>. As the set of constructible numbers is a [[field]], these numbers will be constructible iff <math>\zeta_n</math> is construc ...bers, <math>\zeta_n</math> will be constructible iff there is a chain of [[field extension]]s <math>\mathbb Q = K_0\subseteq K_1\subseteq \cdots\subseteq K_5 KB (926 words) - 17:47, 4 March 2022
- ...ares about the Cyclotomic polynomials begins with the study of splitting [[field]]s. ...''': The extension <math>K</math> of a field <math>F</math> is a splitting field for <math>f(x)\in F[x]</math> if <math>f(x)</math> can be written as the pr8 KB (1,438 words) - 13:50, 23 June 2022