A simplistic approach to inverse transversals

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 q...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 1996-02, Vol.39 (1), p.57-69
Main Authors: Blyth, T. S., Santos, M. H. Almeida
Format: Article
Language:English
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Summary: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091500022781