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Left regular bands of groups of left quotients

Published online by Cambridge University Press:  18 May 2009

Abdulsalam El-Qallali
Abdulsalam El-Qallali
Affiliation:
Department of Mathematics, Al-Fateh University, Tripoli, Lybia.
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In this paper we characterize semigroups S which have a semigroup Q of left quotients, where Q is an ℛ-unipotent semigroup which is a band of groups. Recall that an ℛ-unipotent (or left inverse) semigroup S is one in which every ℛ-class contains a unique idempotent. It is well-known that any ℛ-unipotent semigroup 5 is a regular semigroup in which the set of idempotents is a left regular band in that efe = ef for any idempotents e, fin S. ℛ-unipotent semigroups were studied by several authors, see for example [1] and [13].Bailes [1]characterized ℛ-unipotent semigroups which are bands of groups. This characterization extended the structure of inverse semigroups which are semilattices of groups. Recently, Gould studied in [7]the semigroup S which has a semigroup Q of left quotients where Q is an inverse semigroup which is a semilattice of groups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 29 - 40
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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