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Idempotent-connected abundant semigroups

Published online by Cambridge University Press:  14 November 2011

A. El-Qallali  and
J. B. Fountain
A. El-Qallali
Affiliation:
Department of Mathematics, Al-Fateh University, Tripoli
J. B. Fountain
Affiliation:
Department of Mathematics, University of York
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Synopsis

A general theory for a class of abundant semigroups is developed. For a semigroup S in this class let E be its set of idempotents and <E> the subsemigroup of S generated by E. When <E> is regular there is a homomorphism with a number of desirable properties from S onto a full subsemigroup of the Hall semigroup T<E>. From this fact, analogues of results in the regular case are obtained for *-simple and ℐ*-simple abundant semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 79 - 90
Copyright
Copyright © Royal Society of Edinburgh 1981

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