Completely regular semigroups in the variety generated by the bicyclic semigroup

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1993 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 30, pages 234-240 (issn: 0002-5240, eissn: 1420-8911,

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Authors: Pastijn, Francis; Yan, Xiaoying;

doi: 10.1007/bf01196094

Completely regular semigroups in the variety generated by the bicyclic semigroup

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Abstract

The bicyclic semigroup is a semigroup with identity 1 which can be given by the presentation \(\langle a,b; ab = 1\rangle\). It is shown that the variety generated by the bicyclic semigroup contains a completely regular semigroup iff it is an orthogroup (i.e. its idempotents form a subsemigroup) whose maximal subgroups are abelian.

Related Organizations

Marquette University
United States

Keywords

variety, Free semigroups, generators and relations, word problems, bicyclic semigroup, orthogroup, idempotents, completely regular semigroup, maximal subgroups, Regular semigroups, Varieties and pseudovarieties of semigroups, presentation

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