cyclotomic class

cyclotomic class
мат. циклотомический класс

Большой англо-русский и русско-английский словарь. 2001.

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  • 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

  • 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

  • Cyclotomic unit — In mathematics, a cyclotomic unit is a unit of an algebraic number field of the form (ζn − 1)/(ζ − 1) for ζ a root of unity, or more generally a unit that can be written as a product of these and a root of unity. The… …   Wikipedia

  • Class formation — In mathematics, a class formation is a structure used to organize the various Galois groups and modules that appear in class field theory. They were invented by Emil Artin and John Tate. Contents 1 Definitions 2 Examples of class formations 3 The …   Wikipedia

  • Class field theory — In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields. Most of the central results in this area were proved in the period between 1900 and 1950. The theory takes its name… …   Wikipedia

  • Ideal class group — In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by a certain group known as an ideal class group (or class group). If… …   Wikipedia

  • Root of unity — The 5th roots of unity in the complex plane In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially …   Wikipedia

  • Iwasawa theory — In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Quadratic field — In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q(√d) is a bijection from the set of all square free integers d ≠ 0, 1 to the set of… …   Wikipedia

  • Takagi existence theorem — In class field theory, the Takagi existence theorem states that for any number field K there is a one to one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K ) and the generalized… …   Wikipedia


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