翻訳と辞書 Words near each other ・ Quasi-category ・ Quasi-commutative property ・ Quasi-compact morphism ・ Quasi-constitutionality ・ Quasi-continuous function ・ Quasi-contract ・ Quasi-criminal ・ Quasi-crystals (supramolecular) ・ Quasi-delict ・ Quasi-derivative ・ Quasi-elemental ・ Quasi-empirical method ・ Quasi-empiricism in mathematics ・ Quasi-experiment ・ Quasi-fibration ・ Quasi-finite field ・ Quasi-finite morphism ・ Quasi-foreign corporation ・ Quasi-Frobenius Lie algebra ・ Quasi-Frobenius ring ・ Quasi-Fuchsian group ・ Quasi-geostrophic equations ・ Quasi-harmonic approximation ・ Quasi-Hilda comet ・ Quasi-homogeneous polynomial ・ Quasi-Hopf algebra ・ Quasi-identifier ・ Quasi-invariant measure ・ Quasi-irreversible inhibitor ・ Quasi-isometry Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quasi-finite field ： ウィキペディア英語版 Quasi-finite field In mathematics, a quasi-finite field〔 say that the field satisfies "Moriya's axiom"〕 is a generalisation of a finite field. Standard local class field theory usually deals with complete valued fields whose residue field is ''finite'' (i.e. non-archimedean local fields), but the theory applies equally well when the residue field is only assumed quasi-finite.〔As shown by Mikao Moriya 〕 == Formal definition == A quasi-finite field is a perfect field ''K'' together with an isomorphism of topological groups : $\backslash phi\; :\; \backslash hat\; \backslash to\; \backslash operatorname(K\_s/K),$ where ''K''''s'' is an algebraic closure of ''K'' (necessarily separable because ''K'' is perfect). The field extension ''K''''s''/''K'' is infinite, and the Galois group is accordingly given the Krull topology. The group $\backslash widehat\{\backslash mathbf\{Z\}\}$ is the profinite completion of integers with respect to its subgroups of finite index. This definition is equivalent to saying that ''K'' has a unique (necessarily cyclic) extension ''K''''n'' of degree ''n'' for each integer ''n'' ≥ 1, and that the union of these extensions is equal to ''K''''s''. Moreover, as part of the structure of the quasi-finite field, there is a generator ''F''''n'' for each Gal(''K''''n''/''K''), and the generators must be ''coherent'', in the sense that if ''n'' divides ''m'', the restriction of ''F''''m'' to ''K''''n'' is equal to ''F''''n''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quasi-finite field」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.