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Proper Dubreil-Jacotin inverse semigroups

Published online by Cambridge University Press:  18 May 2009

R. McFadden
R. McFadden
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois 60115, U.S.A.
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This paper is concerned mainly with the structure of inverse semigroups which have a partial ordering defined on them in addition to their natural partial ordering. However, we include some results on partially ordered semigroups which are of interest in themselves. Some recent information [1, 2, 6, 7,11] has been obtained about the algebraic structure of partially ordered semigroups, and we add here to the list by showing in Section 1 that every regular integrally closed semigroup is an inverse semigroup. In fact it is a proper inverse semigroup [10], that is, one in which the idempotents form a complete class modulo the minimum group congruence, and the structure of these semigroups is explicitly known [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975 , pp. 40 - 51
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

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