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Some remarks on modularity of the congruence lattice of regular ω-semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

C. Bonzini  and
A. Cherubini
C. Bonzini
Affiliation:
Universitá, Via Saldini 50, 20133 Milano, Italia, email: bonzini@vmimat.mat.unimi.it
A. Cherubini
Affiliation:
Politecnicó, Piazza L. ad Vinci 32, 20133 Milano, Italia, email: aleche@ipmmal.polimi.it
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Abstract

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In this paper conditions of M-symmetry, strong, semimodularity and θ-modularity for the congruence lattice L (S) of a regular ω-semigroup S are studied. They are proved to be equivalent to modularity. Moreover it is proved that the kernel relation is a congruence on L(S) if and only if L(S) is modular, generalizing an analogous result stated by Petrich for bisimple ω-semigroups.

Keywords

M-symmetric latticestrongly semimodular latticesemimodular latticeθ-modular latticedouble covering propertykernel relationregular ω-semigroup.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 54 - 65
Copyright
Copyright © Australian Mathematical Society 1995

References

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