Quasi-adequate Semigroups

In this thesis, two classes of idempotent-connected quasi-adequate semi-groups are studied. This thesis is divided into two chapters and consists of twointegrated papers.In Chapter 1, we investigate a class of factorisable IC quasi-adequate semi-groups, so-called, factorisable IC quasi-adequate semigroups of type-(H,I). Somecharacterizations of factorisable IC quasi-adequate semigroups of type-(H,I) areobtained. In particular, we prove that any IC quasi-adequate semigroup has afactorisable IC quasi-adequate subsemigroups of type-(H,I) and a band of can-cellative monoids.In Chapter 2, we introduce and study a class of idempotent-connected quasi-adequate semigroups, so-called split IC quasi-adequate semigroups. It is provedthat an IC quasi-adequate semigroup is split if and only if it has an adequatetransversal. The structure of split IC quasi-adequate semigroups whose band ofidempotents are regular bands is obtained. Our results enrich the results obtainedby McAlister and Blyth on split orthodox semigroups.