翻訳と辞書 Words near each other ・ Moduli of algebraic curves ・ Moduli scheme ・ Moduli space ・ Moduli stack of formal group laws ・ Moduli stack of principal bundles ・ Modulidae ・ Modulin ・ Modulo ・ Modulo (jargon) ・ Modulo operation ・ Modulo-N code ・ Modulok (rapper) ・ Modulon ・ Modulor ・ Modulus ・ Modulus (algebraic number theory) ・ Modulus (gastropod) ・ Modulus ambiguus ・ Modulus and characteristic of convexity ・ Modulus bayeri ・ Modulus calusa ・ Modulus carchedonius ・ Modulus guernei ・ Modulus Guitars ・ Modulus modulus ・ Modulus nodosus ・ Modulus of continuity ・ Modulus of convergence ・ Modulus of smoothness ・ Modulus robot 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 Modulus (algebraic number theory) ： ウィキペディア英語版 Modulus (algebraic number theory) In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field. ==Definition== Let ''K'' be a global field with ring of integers ''R''. A modulus is a formal product :$\backslash mathbf\; =\; \backslash prod\_^,\backslash ,\backslash ,\backslash nu(\backslash mathbf)\backslash geq0$ where p runs over all places of ''K'', finite or infinite, the exponents ν(p) are zero except for finitely many p. If ''K'' is a number field, ν(p) = 0 or 1 for real places and ν(p) = 0 for complex places. If ''K'' is a function field, ν(p) = 0 for all infinite places. In the function field case, a modulus is the same thing as an effective divisor, and in the number field case, a modulus can be considered as special form of Arakelov divisor. The notion of congruence can be extended to the setting of moduli. If ''a'' and ''b'' are elements of ''K''×, the definition of ''a'' ≡∗''b'' (mod pν) depends on what type of prime p is: *if it is finite, then ::$a\backslash equiv^\backslash ast\backslash !b\backslash ,(\backslash mathrm\backslash ,\backslash mathbf^\backslash nu)\backslash Leftrightarrow\; \backslash mathrm\_\backslash mathbf\backslash left(\backslash frac-1\backslash right)\backslash geq\backslash nu$ :where ordp is the normalized valuation associated to p; *if it is a real place (of a number field) and ν = 1, then ::$a\backslash equiv^\backslash ast\backslash !b\backslash ,(\backslash mathrm\backslash ,\backslash mathbf)\backslash Leftrightarrow\; \backslash frac>0$ :under the real embedding associated to p. *if it is any other infinite place, there is no condition. Then, given a modulus m, ''a'' ≡∗''b'' (mod m) if ''a'' ≡∗''b'' (mod pν(p)) for all p such that ν(p) > 0. 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「Modulus (algebraic number theory)」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.