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Adequate transversals of quasi-adequate semigroups

By Jehan Al-Bar and James Renshaw

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

Topics: QA
Year: 2012
OAI identifier: oai:eprints.soton.ac.uk:167673
Provided by: e-Prints Soton

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