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On weakly multiplicative inverse transversals

Published online by Cambridge University Press:  20 January 2009

T. S. Blyth  and
M. H. Almeida Santos
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews, Scotland
M. H. Almeida Santos
Affiliation:
Departamento de Matemática, Universidade Nova de Lisboa, Portugal
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Abstract

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We show that an inverse transversal of a regular semigroup is multiplicative if and only if it is both weakly multiplicative and a quasi-ideal. Examples of quasi-ideal inverse transversals that are not multiplicative are known. Here we give an example of a weakly multiplicative inverse transversal that is not multiplicative. An interesting feature of this example is that it also serves to show that, in an ordered regular semigroup in which every element x has a biggest inverse x0, the mapping x↦x00 is not in general a closure; nor is x↦x** in a principally ordered regular semigroup.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 91 - 99
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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