PROFINITE SEMIGROUPS, MALCEV PRODUCTS, AND IDENTITIES

We compute a set of identities defining the Mal'cev product of pseudov arieties of finite semigroups or finite ordered semigroups, We also ch aracterize the pointlike subsets of a finite semigroup by means of a r elational morphism into a profinite semigroup. Finally, we apply our r esults to the proof of the decidability of the Mal'cev products of a d ecidable pseudovariety with the pseudovarieties of nilpotent and of J- trivial semigroups. (C) 1996 Academic Press, Inc.