A Lattice of Varieties of Completely Regular Semigroups
Mario Petrich · Communications in Algebra · 2013
In a previous communication, we defined a countably infinite sequence of varieties of completely regular semigroups, termed canonical. Finite intersections of these varieties constitute the upper ends of the intervals which are the classes of the congruence induced by the complete homomorphism 𝒱 → 𝒱 ∩ ℬ, where ℬ is the variety of all bands. We construct here the lattice generated by the first few of these varieties in some detail. In particular, we determine their bases and illustrate our findings by three diagrams.