Some remarks on modularity of the congruence lattice of regular ω-semigroups
C. Bonzini, A. Cherubini · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1995
Abstract 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.