Some classes of factorizable semigroups
[Almost] factorizable inverse monoids [semigroups] play an important rule in the theory of inverse semigroups (see for example ). The
notion of “factorizable” and “almost factorizable” coincides for inverse
monoids. A couple of crucial results for inverse semigroups S are the
a) S is almost factorizable iff S is an idempotent separating image
of a semidirect product G*Y of a semilattice Y by a group G;
b) S is isomorphic to some G*Y iff S is both E-unitary and almost
In the first part of this talk we will present the concepts involved
in the inverse case, and in second we shall show how this theory of
[almost] factorizable inverse monoids [semigroups] extend to the wider
classes of weakly ample monoids [semigroups], which are a type of
(2, 1, 1)-algebras that include, in particular, the inverse semigroups.
These latter results appear in a joint paper with M´aria B. Szendrei .
Gracinda Gomes (CAUL/Mat. FCUL)
June 12, 2007