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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 Orthodox semigroup ： ウィキペディア英語版 Orthodox semigroup In mathematics, an orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular ''E''-semigroup.〔J. Almeida, J.-E. Pin and P. Weil (Semigroups whose idempotents form a subsemigroup ) updated version of 〕 The term ''orthodox semigroup'' was coined by T. E. Hall and presented in a paper published in 1969. Certain special classes of orthodox semigroups have been studied earlier. For example, semigroups which are also unions of groups, in which the sets of idempotents form subsemigroups were studied by P. H. H. Fantham in 1960. ==Examples== *Consider the binary operation in the set ''S'' = defined by the following Cayley table : :Then ''S'' is an orthodox semigroup under this operation, the subsemigroup of idempotents being .〔 *Inverse semigroups and bands are examples of orthodox semigroups. 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「Orthodox semigroup」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.