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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 Primordial element (algebra) ： ウィキペディア英語版 Primordial element (algebra) In algebra, a primordial element is a particular kind of a vector in a vector space. Let ''V'' be a vector space over a field ''k'' and fix a basis for ''V'' of vectors $e\_i$ for $i\; \backslash in\; I$. By the definition of a basis, every vector ''v'' in ''V'' can be expressed uniquely as :$v\; =\; \backslash sum\_\; a\_i(v)\; e\_i.$ Define $I(v)\; =\; \backslash$, the set of indices for which the expression of ''v'' has a nonzero coefficient. Given a subspace ''W'' of ''V'', a nonzero vector ''w'' in ''W'' is said to be "primordial" if it has the following two properties:〔Milne, J., (Class field theory course notes ), updated March 23, 2013, Ch IV, §2.〕 #$I(w)$ is minimal among the sets $I(w\text{'})$, $0\; \backslash ne\; w\text{'}\; \backslash in\; W$ and #$a\_i(w)\; =\; 1$ for some ''i''. == References == 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「Primordial element (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.