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The set of idempotents of a completely regular semigroup as a binary algebra

Published online by Cambridge University Press:  17 April 2009

Raymond Broeksteeg
Raymond Broeksteeg
Affiliation:
Mathematics DepartmentMonash University ClaytonVic 3168Australia e-mail: apm485g@vaxc.cc.monash.edu.au
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Abstract

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A semigroup S is called E-solid if and only if for all idempotents e, f, g ∈ S such that e L f R g there exists an idempotent h ∈ S such that e R h L g. Each completely regular semigroup is E-solid. We characterise the idempotents of an arbitrary E-solid regular semigroup as a set with a binary operation on it satisfying a given finite set of identities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 91 - 107
Copyright
Copyright © Australian Mathematical Society 1994

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