J Austral Math Soc Ser A 58 pp54--65, 1995.

Some Remarks on Modularity of the Congruence Lattice of Regular w-Semigroups

C. Bonzini and A. Cherubini

(Received 14 April 1992; revised 10 August 1992)

Abstract

In this paper conditions of M-symmetry, strong, semimodularity and q-modularity for the congruence lattice L(S) of a regular w-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 w-semigroups.

1991 AMS Subject Classification: 20M10

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Authors

C. Bonzini: Universita, Via Saldini 50, 20133 Milano, Italia.
mailto:bonzini@vmimat.mat.unimi.it
A. Cherubini: Politecnico, Piazza L. ad Vinci 32, 20133 Milano, Italia.
mailto:aleche@ipmma1.polimi.it

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Last Modified: Thu Jan 9 9:04:23 2003