M-Solid Varieties of Languages

In this paper, a characterization of the language varieties and congruence varieties corresponding toM -solid pseudovarieties is presented. Taking into account the isomorphisms of the Eilenberg-type correspondences, each complete sublattice of pseudovarieties corresponds to a complete sublattice of language varieties, as well as another one of congruence varieties. For the varieties of tree language, we present the complete sublattices of varieties of languages and the complete sublattice of varieties of congruences isomorphic to the complete sublattice of all M -solid pseudovarieties.