Lattices of completely regular semigroup varieties
Francis J. Pastijn, Peter G. Trotter · Pacific Journal of Mathematics · 1985
Let p be a fully invariant congruence on the free completely regular semigroup F£ R of countably infinite rank.Let p min and p min be the least congruences on Fχ R with respectively the same trace and the same kernel as p.Let p max and p max be the greatest congruences on Fχ R with respectively the same trace and the same kernel as p.These congruences are shown to be fully invariant.We construct a network of varieties corresponding to the congruences , p max , p max ,p, p min , p min , (ft™) 1 ™, (ρ mm ) min , and their intersections.Intervals between successive joins of the network, in the lattice of subvarieties of completely regular semigroups, are characterised as direct products of particular subintervals.By comparing the network with the chain of varieties that are each generated by a free completely regular semigroup of finite rank we get information on the network and the chain.