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Eventually regular semigroups

Published online by Cambridge University Press:  17 April 2009

P.M. Edwards
P.M. Edwards
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
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Abstract

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A semigroup is said to be eventually regular if each of its elements has some power that is regular. Regular and group-bound semigroups are each eventually regular. Idempotent-surjective semigroups are semigroups such that all idempotent congruence classes contain idempotents; eventually regular semigroups are idempotent-surjective. Many results for regular semigroups also hold for eventually regular semigroups or even for idempotent-surjective semigroups and so in particular are also valid for group-bound semigroups. Lallement's lemma is generalized to eventually regular semigroups and the maximum idempotent-separating congruence on such a semigroup is found. Other congruences are considered and the results obtained are applied to yield results on biordered sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 23 - 38
Copyright
Copyright © Australian Mathematical Society 1983

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