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A simplistic approach to inverse transversals*

Published online by Cambridge University Press:  20 January 2009

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

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An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element of S. In the literature there are three known types of inverse transversal, namely those that are multiplicative, those that are weakly multiplicative, and those that form quasi-ideals. Here, by considering natural ways in which certain words can be simplified, we reveal four new types of inverse transversal. All of these can be illustrated nicely in examples that are based on 2 × 2 matrices.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 57 - 69
Copyright
Copyright © Edinburgh Mathematical Society 1996

Footnotes

*

NATO Collaborative Research Grant 910765 is gratefully acknowledged.

References

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