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
905-930
Al-Bar, Jehan
f9a3238a-9228-413c-8f75-171d6f194422
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
29 February 2012
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), .
(doi:10.1080/00927872.2010.543205).
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: http://eprints.soton.ac.uk/id/eprint/167673
ISSN: 0092-7872
PURE UUID: 9c54235e-3329-4483-ba58-67d0ae669de2
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Date deposited: 16 Nov 2010 17:03
Last modified: 14 Mar 2024 02:34
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Author:
Jehan Al-Bar
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