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- Biordered_set abstract "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.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.".
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- Biordered_set wikiPageLength "12777".
- Biordered_set wikiPageOutDegree "27".
- Biordered_set wikiPageRevisionID "635411149".
- Biordered_set wikiPageWikiLink Axiom.
- Biordered_set wikiPageWikiLink Binary_operation.
- Biordered_set wikiPageWikiLink Binary_relation.
- Biordered_set wikiPageWikiLink Category:Algebraic_structures.
- Biordered_set wikiPageWikiLink Category:Mathematical_structures.
- Biordered_set wikiPageWikiLink Category:Semigroup_theory.
- Biordered_set wikiPageWikiLink David_Easdown.
- Biordered_set wikiPageWikiLink Direct_sum.
- Biordered_set wikiPageWikiLink Domain_(mathematics).
- Biordered_set wikiPageWikiLink Domain_of_a_function.
- Biordered_set wikiPageWikiLink Dual_(mathematics).
- Biordered_set wikiPageWikiLink Duality_(mathematics).
- Biordered_set wikiPageWikiLink E-dense_semigroup.
- Biordered_set wikiPageWikiLink E-inversive_semigroup.
- Biordered_set wikiPageWikiLink Idempotence.
- Biordered_set wikiPageWikiLink Idempotent.
- Biordered_set wikiPageWikiLink Internal_direct_sum.
- Biordered_set wikiPageWikiLink K._S._S._Nambooripad.
- Biordered_set wikiPageWikiLink K_S_S_Nambooripad.
- Biordered_set wikiPageWikiLink Linear_subspace.
- Biordered_set wikiPageWikiLink Mathematical_object.
- Biordered_set wikiPageWikiLink Partial_function.
- Biordered_set wikiPageWikiLink Preorder.
- Biordered_set wikiPageWikiLink Proposition_(mathematics).
- Biordered_set wikiPageWikiLink Quasiorder.
- Biordered_set wikiPageWikiLink Reflexive_relation.
- Biordered_set wikiPageWikiLink Regular_semigroup.
- Biordered_set wikiPageWikiLink Relation_(mathematics).
- Biordered_set wikiPageWikiLink Semigroup.
- Biordered_set wikiPageWikiLink Set_(mathematics).
- Biordered_set wikiPageWikiLink Structure.
- Biordered_set wikiPageWikiLink Symmetric_relation.
- Biordered_set wikiPageWikiLink Theorem.
- Biordered_set wikiPageWikiLink Transitive_relation.
- Biordered_set wikiPageWikiLink Vector_space.
- Biordered_set wikiPageWikiLinkText "Biordered set".
- Biordered_set wikiPageWikiLinkText "biorder relation".
- Biordered_set wikiPageWikiLinkText "biordered set".
- Biordered_set hasPhotoCollection Biordered_set.
- Biordered_set wikiPageUsesTemplate Template:Clarify.
- Biordered_set wikiPageUsesTemplate Template:Inappropriate_tone.
- Biordered_set wikiPageUsesTemplate Template:Reflist.
- Biordered_set subject Category:Algebraic_structures.
- Biordered_set subject Category:Mathematical_structures.
- Biordered_set subject Category:Semigroup_theory.
- Biordered_set hypernym Object.
- Biordered_set type Article.
- Biordered_set type Planet.
- Biordered_set type Article.
- Biordered_set type Concept.
- Biordered_set comment "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.".
- Biordered_set label "Biordered set".
- Biordered_set sameAs m.05t02gk.
- Biordered_set sameAs Q4915231.
- Biordered_set sameAs Q4915231.
- Biordered_set wasDerivedFrom Biordered_set?oldid=635411149.
- Biordered_set isPrimaryTopicOf Biordered_set.