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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 Basis (universal algebra) ： ウィキペディア英語版 Basis (universal algebra) In universal algebra a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner. It also represents the endomorphisms of an algebra by certain indexings of algebra elements, which can correspond to the usual matrices when the free algebra is a vector space. == Definitions == The basis (or reference frame) of a (universal) algebra is a function ''b'' that takes some algebra elements as values $b(i)$ and satisfies either one of the following two equivalent conditions. Here, the set of all $b(i)$ is called basis set, whereas several authors call it the "basis".〔Gould.〕〔Grätzer 1968, p.198.〕 The set $I$ of its arguments ''i'' is called dimension set. Any function, with all its arguments in the whole $I$, that takes algebra elements as values (even outside the basis set) will be denoted by ''m''. Then, ''b'' will be an ''m''. 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「Basis (universal algebra)」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.