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The breadth of the lattice of those varieties of inverse semigroups which contain the variety of groups

Published online by Cambridge University Press:  14 November 2011

Norman R. Reilly
Norman R. Reilly
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada
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Synopsis

The relations v1 and v2 defined on the lattice ℒ of varieties of inverse semigroups by v1 if and only if and v2 if and only if , where denotes tie variety of groups, are both congruences on ℒ the class v1, is simply the lattice of varieties of grcups and is therefore known to have cardinality .

The class v2 is precisely the sublattice of ℒ consisting of those varieties containing . Each v1-class contains preciselyone element of v2. The main result of this paper establishes that the sublattice v2 of ℒ has breadth . From this it follows that the lattice ℒ/v1 also has breadth . Some consequences concerning varieties generated by fundamental inverse semigroups are also considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 319 - 325
Copyright
Copyright © Royal Society of Edinburgh 1983

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