On automorphisms of transformation semigroups
Degree GrantorUniversity of Canterbury
Degree NameResearch report
This paper addresses the problem of describing automorphisms of semigroups of transformations. In  we were involved in characterizing all automorphisms of CroisotTeissier semigroups. The semigroups of transformations that belong to this large family generally consist of many-to-one transformations whose restrictions to range sets are oneto- one. Here we consider enlargements of Croisot-Teissier semigroups whose elements, restricted to range-sets, are no longer one-to-one. We show that such semigroups contain a maximal Croisot-Teissier semigroup, which in turn is used to present a complete description of automorphisms of these semigroups. Moreover we describe the Green's relations on these enlargements of Croisot-Teissier semigroups, and show that they are in fact simple semigroups, whose regular elements form a bisimple subsemigroup. We start by recalling the definition of Croisot-Teissier semigroups.
SubjectsField of Research::01 - Mathematical Sciences
- Engineering: Reports