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On the compatibility of the natural order on a regular semigroup

Published online by Cambridge University Press:  14 November 2011

T. S. Blyth  and
Gracinda M. S. Gomes
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
Gracinda M. S. Gomes
Affiliation:
Mathematical Institute, University of St Andrews
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Synopsis

A notable achievement in the algebraic theory of semigroups has been the discovery by Nambooripad of the natural order on a regular semigroup. He has shown that this order is compatible with multiplication if and only if the semigroup is locally inverse, in the sense that every local submonoid is an inverse semigroup. In this paper we determine precisely when the natural order is compatible on the right (respectively left) with multiplication; this is so if and only if every local submonoid is ℒ-unipotent (respectively ℛ-unipotent).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 79 - 84
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

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