HS-stability and complex products in involution semigroups

Semigroup Forum - When does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing...     

Free idempotent generated semigroups: subsemigroups,retracts and maximal subgroups

Let S be a subsemigroup of a semigroup T and let IG(E) and IG(F) be the free idempotent generated semigroups over the biordered sets of idempotents of E of S and F of T, respectively. We examine the relationship between IG(E) and IG(F), including the case where S is a retract of T. We give su?cient conditions satisfied by T and S such that for any e∈E, the maximal subgroup of IG(E) with identity e is isomorphic to the corresponding maximal subgroup of IG(F). We then apply this result to some special cases and, in particular, to that of the partial endomorphism monoid PEnd A and the endomorphism monoid EndA of an independence algebra A of finite rank. As a corollary, we obtain Dolinka’s reduction result for the case where A is a finite set.     

$$\aleph _0$$ -categoricity of semigroups II

Semigroup Forum - A countable semigroup is $$\aleph _0$$ -categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into...