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Primitive inverse congruences on categorical semigroups

Published online by Cambridge University Press:  20 January 2009

John Fountain  and
Gracinda M. S. Gomes
John Fountain
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD, UK
Gracinda M. S. Gomes
Affiliation:
Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749–016, Lisboa, Portugal and Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649–003 Lisboa, Portugal
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Abstract

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We give an abstract description of the kernel of a proper primitive inverse congruence on a categorical semigroup. More specifically, we show that it is a *-reflexive, *-unitary, *-dense subsemigroup, and that on a given categorical semigroup there is a one–one correspondence between such subsemigroups and the proper primitive inverse congruences. Our results allow us to give a description of the minimum proper primitive inverse semigroup congruence on a strongly E*-dense categorical semigroup.

Keywords

congruenceinverse semigroupprimitive idempotents
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 395 - 413
Copyright
Copyright © Edinburgh Mathematical Society 2000

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