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Adequate transversals of quasi-adequate semigroups

Adequate transversals of quasi-adequate semigroups
Adequate transversals of quasi-adequate semigroups
The concept of an adequate transversal of an abundant semigroup was introduced by El-Qallali in [5] whilst in [4] he and Fountain initiated the study of quasi-adequate semigroups as natural generalisations of orthodox semigroups. In this work we provide a structure theorem for adequate transversals of certain types of quasi-adequate semigroup and from this deduce Saito's classic result on the structure of inverse transversals of orthodox semigroups. We also apply it to left ample adequate transversals of left adequate semigroups and provide a structure for these based on semidirect products of adequate semigroups by left regular bands.
abundant semigroup, adequate, quasi-adequate, left adequate, left ample, adequate transversal, semidirect product, inverse transversal, regular semigroup
0092-7872
905-930
Al-Bar, Jehan
f9a3238a-9228-413c-8f75-171d6f194422
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Al-Bar, Jehan
f9a3238a-9228-413c-8f75-171d6f194422
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c

Al-Bar, Jehan and Renshaw, James (2012) Adequate transversals of quasi-adequate semigroups. Communications in Algebra, 40 (3), 905-930. (doi:10.1080/00927872.2010.543205).

Record type: Article

Abstract

The concept of an adequate transversal of an abundant semigroup was introduced by El-Qallali in [5] whilst in [4] he and Fountain initiated the study of quasi-adequate semigroups as natural generalisations of orthodox semigroups. In this work we provide a structure theorem for adequate transversals of certain types of quasi-adequate semigroup and from this deduce Saito's classic result on the structure of inverse transversals of orthodox semigroups. We also apply it to left ample adequate transversals of left adequate semigroups and provide a structure for these based on semidirect products of adequate semigroups by left regular bands.

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Published date: 29 February 2012
Keywords: abundant semigroup, adequate, quasi-adequate, left adequate, left ample, adequate transversal, semidirect product, inverse transversal, regular semigroup

Identifiers

Local EPrints ID: 167673
URI: https://eprints.soton.ac.uk/id/eprint/167673
ISSN: 0092-7872
PURE UUID: 9c54235e-3329-4483-ba58-67d0ae669de2
ORCID for James Renshaw: ORCID iD orcid.org/0000-0002-5571-8007

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Date deposited: 16 Nov 2010 17:03
Last modified: 27 Jul 2019 00:38

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