On the lattice of sub-pseudovarieties of DA

Manfred Kufleitner (1) , Pascal Weil (2)

1 Institut für Formale Methoden der Informatik
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The wealth of information that is available on the lattice of varieties of bands, is used to illuminate the structure of the lattice of sub-pseudovarieties of DA, a natural generalization of bands which plays an important role in language theory and in logic. The main result describes a hierarchy of decidable sub-pseudovarieties of DA in terms of iterated Mal'cev products with the pseudovarieties of definite and reverse definite semigroups.

Mots clés: pseudovarieties; bands

Domaines: Théorie des groupes [math.GR]

Manfred Kufleitner, Pascal Weil. On the lattice of sub-pseudovarieties of DA. Semigroup Forum, 2010, 81, pp.243-254. ⟨hal-00376641v2⟩