Complete Congruences on the Lattice of Rees–Sushkevich Varieties
Norman R. Reilly · Communications in Algebra · 2007
We study the lattice ℒ(RSn) of subvarieties of the variety of semigroups generated by completely 0-simple semigroups over groups with exponent dividing n, with a particular focus on the lattice ℒℰ(RSn) consisting of those varieties that are generated by completely 0-simple semigroups. The sublattice of ℒℰ(RSn) consisting of the aperiodic varieties is described and several endomorphisms of ℒ(RSn) considered. The complete congruence on ℒℰ(RSn) that relates varieties containing the same aperiodic completely 0-simple semigroups is considered in some detail.