cyclotomic extension

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• Extension (mathematics) — In mathematics, the word extension has many uses. See:Analysis* Carathéodory s extension theorem * Continuous linear extension * M. Riesz extension theorem * Krein extension theorem * Hahn Banach theoremAlgebra* Abelian extension * Algebraic… …   Wikipedia

• Extension Cyclotomique — En théorie algébrique des nombres, on appelle extension cyclotomique du corps des nombres rationnels, les surcorps de la forme où ζn est une racine primitive nème de l unité ; cette appellation provient de ce que ces extensions sont des… …   Wikipédia en Français

• Cyclotomic field — In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Q, the field of rational numbers. The n th cyclotomic field Q(ζn) (with n > 2) is obtained by adjoining a primitive n… …   Wikipedia

• Extension cyclotomique — En théorie algébrique des nombres, on appelle extension cyclotomique du corps Q des nombres rationnels tout corps de rupture d un polynôme cyclotomique, i.e. tout corps de la forme Q(ζ) où ζ est une racine de l unité. Ces corps jouent un rôle… …   Wikipédia en Français

• Abelian extension — In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is a cyclic group, we have a cyclic extension. More generally, a Galois extension is called solvable if its Galois group is… …   Wikipedia

• Inverse Galois problem — In mathematics, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th centuryFact|date=February 2007, is… …   Wikipedia

• Class number formula — In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function Contents 1 General statement of the class number formula 2 Galois extensions of the rationals 3 A …   Wikipedia

• Algebraically closed field — In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F , has a root in F . ExamplesAs an example, the field of real numbers is not algebraically closed,… …   Wikipedia

• Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   Wikipedia

• Conductor-discriminant formula — In mathematics, the conductor discriminant formula is a formula calculating the discriminant of a finite Galois extension L / K of global fields from the global Artin conductors of the irreducible characters Irr(G) of the Galois group G = G(L /… …   Wikipedia

• Corps cyclotomique — Extension cyclotomique En théorie algébrique des nombres, on appelle extension cyclotomique du corps des nombres rationnels, les surcorps de la forme où ζn est une racine primitive nème de l unité ; cette appellation provient de ce que ces… …   Wikipédia en Français