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Semigroups with zero whose idempotents form a subsemigroup

Published online by Cambridge University Press:  14 November 2011

Gracinda M. S. Gomes  and
John M. Howie
Gracinda M. S. Gomes
Affiliation:
Centro de Algebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa, Portugal
John M. Howie
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, U.K.
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Abstract

The structure of a categorical, E*-dense, E*-unitary E-semigroup S is elucidated in terms of a ‘B-quiver’, where B is a primitive inverse semigroup. In the case where S is strongly categorical, B is a Brandt semigroup. A covering theorem is also proved, to the effect that every categorical E*-dense E-semigroup has a cover which is a categorical, E*-dense, E*-unitary E-semigroup.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 265 - 281
Copyright
Copyright © Royal Society of Edinburgh 1998

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