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Rees matrix covers for a class of abundant semigroups

Published online by Cambridge University Press:  14 November 2011

Mark V. Lawson
Mark V. Lawson
Affiliation:
Lincoln College, Oxford OX1 3DR, U.K
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Synopsis

Recently considerable attention has been paid to the study of locally inverse regular semigroups. McAlister [14] obtained a description of such semigroups as locally isomorphic images of regular Rees matrix semigroups over an inverse semigroup. The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic analogue of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP rings are abundant. The aim of this paper is to show how the structure theory described above for regular semigroups may be generalised to a class of abundant semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 109 - 120
Copyright
Copyright © Royal Society of Edinburgh 1987

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