class field

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• 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

• Non-abelian class field theory — In mathematics, non abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and classical set of results on abelian extensions of any number field K, to the general Galois… …   Wikipedia

• Hilbert class field — In algebraic number theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K . Its degree over K equals the class number of K and the Galois group of E over K is canonically isomorphic to the ideal… …   Wikipedia

• Local class field theory — In mathematics, local class field theory is the study in number theory of the abelian extensions of local fields. It is in itself a rather successful theory, leading to definite conclusions. It is also important for (and was developed to help… …   Wikipedia

• Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… …   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 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

• field trip — noun a group excursion (to a museum or the woods or some historic place) for firsthand examination • Hypernyms: ↑excursion, ↑jaunt, ↑outing, ↑junket, ↑pleasure trip, ↑expedition, ↑sashay * * * noun …   Useful english dictionary

• Field Target — is an outdoor air gun discipline originating in the United Kingdom, on the late 1980s, but gaining popularity worldwide.UK RulesIn UK (United Kingdom) rules, competitors aim to shoot the small “kill” zone that forms part of a larger metal… …   Wikipedia

• Class Action (film) — Class Action Theatrical release poster Directed by Michael Apted Produced by …   Wikipedia

• Field Day — is an annual amateur radio exercise, widely sponsored by IARU regions and member organizations, encouraging emergency communications preparedness among amateur radio operators. In the United States, it is typically the largest single emergency… …   Wikipedia