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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 Incidence algebra ： ウィキペディア英語版 Incidence algebra In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative ring with unity. ==Definition== A locally finite poset is one for which every closed interval :(b'' ) = within it is finite. The members of the incidence algebra are the functions ''f'' assigning to each nonempty interval (b'' ) a scalar ''f''(''a'', ''b''), which is taken from the ''ring of scalars'', a commutative ring with unity. On this underlying set one defines addition and scalar multiplication pointwise, and "multiplication" in the incidence algebra is a convolution defined by :$(f$ *g)(a, b)=\sum_f(a, x)g(x, b). An incidence algebra is finite-dimensional if and only if the underlying poset is finite. 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「Incidence 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.