论文信息 - Complete Congruences on Lattices of Varieties and of Pseudovarieties

Complete Congruences on Lattices of Varieties and of Pseudovarieties

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.

Peter G. Trotter | Francis Pastijn

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