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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Exponential field ： ウィキペディア英語版 Exponential field In mathematics, an exponential field is a field that has an extra operation on its elements which extends the usual idea of exponentiation. ==Definition== A field is an algebraic structure composed of a set of elements, ''F'', two binary operations, addition (+) such that ''F'' forms an abelian group with identity 0''F'' and multiplication (·), such that ''F'' excluding 0''F'' forms an abelian group under multiplication with identity 1''F'', and such that multiplication is distributive over addition, that is for any elements ''a'', ''b'', ''c'' in ''F'', one has . If there is also a function ''E'' that maps ''F'' into ''F'', and such that for every ''a'' and ''b'' in ''F'' one has : then ''F'' is called an exponential field, and the function ''E'' is called an exponential function on ''F''.〔Helmut Wolter, ''Some results about exponential fields (survey)'', Mémoires de la S.M.F. 2e série, 16, (1984), pp.85–94.〕 Thus an exponential function on a field is a homomorphism from the additive group of ''F'' to its multiplicative group. 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「Exponential 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.