Complete Congruences on Lattices of Varieties and of Pseudovarieties
Francis J. Pastijn, Peter G. Trotter · International Journal of Algebra and Computation · 1998
Three methods for the construction of all complete congruences on the lattice Lv( V ) of subvarieties of a variety V are introduced. It is shown that there exists an order preserving embedding of the lattice of complete congruences on the lattice Lp( P ) of all subpseudovarieties of a given pseudovariety P into the direct product of the lattices of complete congruences on lattices of subvarieties of varieties generated by members of P; thus there are methods for constructing all complete congruences on Lp( P ). By way of application, 2ℵ0 complete congruences and complete endomorphisms are constructed on any lattice Lv( V ), where V is a certain epigroup variety which includes all bands; there is an analogous application for the lattice of all pseudovarieties of semigroups.