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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 Light's associativity test ： ウィキペディア英語版 Light's associativity test In mathematics, Light's associativity test is a procedure invented by F W Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. Direct verification of the associativity of a binary operation specified by a Cayley table is cumbersome and tedious. Light's associativity test greatly simplifies the task. ==Description of the procedure== Let a binary operation ' · ' be defined in a finite set ''A'' by a Cayley table. Choosing some element ''a'' in ''A'', two new binary operations are defined in ''A'' as follows: :''x'' $\backslash star$ ''y'' = ''x'' · ( ''a'' · ''y'' ) :''x'' $\backslash circ$ ''y'' = ( ''x'' · ''a'' ) · ''y'' The Cayley tables of these operations are constructed and compared. If the tables coincide then ''x'' · ( ''a'' · ''y'' ) = ( ''x'' · ''a'' ) · ''y'' for all ''x'' and ''y''. This is repeated for every element of the set ''A''. The example below illustrates a further simplification in the procedure for the construction and comparison of the Cayley tables of the operations ' $\backslash star$ ' and ' $\backslash circ$ '. It is not even necessary to construct the Cayley tables of ' $\backslash star$ ' and ' $\backslash circ$ ' for ''all'' elements of ''A''. It is enough to compare Cayley tables of ' $\backslash star$ ' and ' $\backslash circ$ ' corresponding to the elements in a proper generating subset of ''A''. 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「Light's associativity test」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.