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On left quasinormal orthodox semigroups

Published online by Cambridge University Press:  14 November 2011

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

The existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroup S is locally inverse and orthodox if and only if there exists a local isomorphism from S onto an inverse semigroup T.

In this paper, we show the existence of a smallest R-unipotent congruence ρ on an orthodox semigroup S and give its expression in the case where S is also left quasinormal. Finally, we prove that a regular semigroup S is left quasinormal and orthodox if and only if there exists a local isomorphism from S onto an R-unipotent semigroup T.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 59 - 71
Copyright
Copyright © Royal Society of Edinburgh 1983

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