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A finitely generated variety of combinatorial inverse semigroups having uncountably many subvarieties

Published online by Cambridge University Press:  12 July 2007

Jiří Kad'ourek
Jiří Kad'ourek
Affiliation:
Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic ([email protected])
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Abstract

A finite combinatorial inverse semigroup Θ of moderate size is presented such that the variety of combinatorial inverse semigroups generated by Θ possesses the following properties. The lattice of all subvarieties of this variety has the cardinality of the continuum. Moreover, this semigroup Θ, and hence also the variety it generates and its subvarieties, all have E-unitary covers over any non-trivial variety of groups. This indicates that the mentioned uncountable sublattice appears quite near the bottom of the lattice of all varieties of combinatorial inverse semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 6 , December 2002 , pp. 1373 - 1394
Copyright
Copyright © Royal Society of Edinburgh 2002

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