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Semigroups whose idempotents form a subsemigroup

Published online by Cambridge University Press:  24 October 2008

J. Almeida ,
J.-E. Pin  and
P. Weil
J. Almeida
Affiliation:
Centro de Matemtica, Universidade do Porto, 4000 Porto, Portugal
J.-E. Pin
Affiliation:
LITP, Universit Paris 6 et CNRS, Tour 5565, 4 place Jussieu, 75252 Paris Cedex 05, France
P. Weil
Affiliation:
LITP, Universit Paris 6 et CNRS, Tour 5565, 4 place Jussieu, 75252 Paris Cedex 05, France
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Abstract

We prove that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to those of Birget, Margolis and Rhodes, and of Jones and Szendrei on finite E-semigroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 241 - 253
Copyright
Copyright © Cambridge Philosophical Society 1992

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