A Study On The Expansion Of Complete Regular Semigroups

In the thesis, we mainly research the structure and properties of the inflation of some com-pletely regular semigroups. There are totally four chapters.In chapter one, we mainly introduce the research background and the basic concepts involved.In chapter two, we firstly begin with basic properties of the inflation of some completely regular semigroups. It’s convenient to discuss the generalization of the strong semilattice structure. Then we define a partial order relation of the inflation of completely regular semigroups and study its properties.In chapter three, the inflation of normal orthocryptogroups is discussed. In the first section, we briefly introduce the properties of normal orthocryptogroups. In the second, we study the in-flation of normal orthocryptogroups. By introducing a new semilattice decomposition which is a quasi-strong semilattice, the quasi-strong semilattice characterizations of the inflation of nor-mal orthocryptogroups are given. As an application of this conclusion, the inflation of Clifford semigroups is also described. In the third, we use the obtained structure to research the homomor-phism between the inflation of normal orthocryptogroups. Some related conclusions in regular semigroups are generalized.In chapter four, the inflation of regular bands is studied. In this thesis, the structure of G-strong semilattice in regular semigroups is generalized. Via a new semilattice decomposition structure namely πG-strong semilattice, some features of the inflation of regular bands are ob-tained and a structure theorem of inflation of regular bands is established. As applications, we give construction theorems the inflation of bands which are right quasi-normal, left quasi normal and normal bands. Finally, we discusse the homomorphism between the inflation of regular bands.