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A biordered set ("boset") is a mathematical object that occurs in the description of the structure of the set of idempotents in a semigroup. The concept and the terminology were developed by K S S Nambooripad in the early 1970s. The defining properties of a biordered set are expressed in terms of two quasiorders defined on the set and hence the name biordered set. Patrick Jordan, while a master's student at University of Sydney, introduced in 2002 the term boset as an abbreviation of biordered set.〔Patrick K. Jordan. ''On biordered sets, including an alternative approach to fundamental regular semigroups''. Master’s thesis, University of Sydney, 2002.〕 According to Mohan S. Putcha, "The axioms defining a biordered set are quite complicated. However, considering the general nature of semigroups, it is rather surprising that such a finite axiomatization is even possible." Since the publication of the original definition of the biordered set by Nambooripad, several variations in the definition have been proposed. David Easdown simplified the definition and formulated the axioms in a special arrow notation invented by him. The set of idempotents in a semigroup is a biordered set and every biordered set is the set of idempotents of some semigroup.〔 A regular biordered set is a biordered set with an additional property. The set of idempotents in a regular semigroup is a regular biordered set, and every regular biordered set is the set of idempotents of some regular semigroup.〔 == Definition == The formal definition of a biordered set given by Nambooripad〔 requires some preliminaries. 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「biordered set」の詳細全文を読む スポンサード リンク
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