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Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

D. B. Mcalister
D. B. Mcalister
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115, U.S.A.
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Abstract

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A partially ordered semigroup S is said to be a Dubreil-Jacotin semigroup if there is an isotone homomorphism θ of S onto a partially ordered group such that {} has a greatest member. In this paper we investigate the structure of regular Dubreil-Jacotin semigroups in which the imposed partial order extends the natural partial order on the idempotents. The main tool used is a local structure theorem which is introduced in Section 2. This local structure theorem applies to many other contexts as well.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 325 - 336
Copyright
Copyright © Australian Mathematical Society 1981

References

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