Quasi-ideal transversals of abundant semigroups and spined products
Quasi-ideal transversals of abundant semigroups and spined products
We provide a new and much simpler structure for quasi-ideal adequate transversals of abundant semigroups in terms of spined products, which is similar in nature to that given by Saito for weakly multiplicative inverse transversals of regular semigroups [10]. As a consequence we deduce a similar result for multiplicative transversals of abundant semigroups and also consider the case when the semigroups are in fact regular and provide some new structure theorems for inverse transversals.
abundant semigroup, adequate semigroup, adequate transversal, spined product, quasi-ideal, multiplicative, inverse transversal, regular semigroup
522-537
Al-Bar, Jehan
f9a3238a-9228-413c-8f75-171d6f194422
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
21 November 2011
Al-Bar, Jehan
f9a3238a-9228-413c-8f75-171d6f194422
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Al-Bar, Jehan and Renshaw, James
(2011)
Quasi-ideal transversals of abundant semigroups and spined products.
Semigroup Forum, 83 (3), .
(doi:10.1007/s00233-010-9223-4).
Abstract
We provide a new and much simpler structure for quasi-ideal adequate transversals of abundant semigroups in terms of spined products, which is similar in nature to that given by Saito for weakly multiplicative inverse transversals of regular semigroups [10]. As a consequence we deduce a similar result for multiplicative transversals of abundant semigroups and also consider the case when the semigroups are in fact regular and provide some new structure theorems for inverse transversals.
Text
quasi_ideals.pdf
- Author's Original
More information
Submitted date: 17 June 2009
Accepted/In Press date: 17 June 2009
Published date: 21 November 2011
Keywords:
abundant semigroup, adequate semigroup, adequate transversal, spined product, quasi-ideal, multiplicative, inverse transversal, regular semigroup
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 66453
URI: http://eprints.soton.ac.uk/id/eprint/66453
ISSN: 0037-1912
PURE UUID: 5827e2d3-8f2f-43f8-b827-275622c28968
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Date deposited: 18 Jun 2009
Last modified: 14 Mar 2024 02:34
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Author:
Jehan Al-Bar
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