Profinite semigroups, Mal'cev products and identities

Jean-Eric Pin (1) , Pascal Weil (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We compute a set of identities defining the Mal'cev product of pseudovarieties of finite semigroups or finite ordered semigroups. We also characterize the pointlike subsets of a finite semigroup by means of a relational morphism into a profinite semigroup. Finally, we apply our results to the proof of the decidability of the Mal'cev products of a decidable pseudovariety with the pseudovarieties of nilpotent and of J-trivial semigroups.

Mots clés: Profinite semigroups; Mal'cev products; identities

Domaines: Théorie des groupes [math.GR]; Mathématique discrète [cs.DM]

Jean-Eric Pin, Pascal Weil. Profinite semigroups, Mal'cev products and identities. Journal of Algebra, 1996, 182 (3), pp.604-626. ⟨hal-00143953⟩