Some Studies On Weakly Regular *-Semigroups

We study weakly regular *-semigroups and quasi regular *-semigroups in thisthesis which is divided into five parts.The first part is a brief introduction. We show the research background andresearch content of this paper.In the second part, We prove that D-class of a weakly regular *-semigroup issquare.In the third part, semidirect products and subdirect products of weakly regular*-semigroups are studied, and a construction of all subdirect products of weaklyregular *-semigroups is obtained. As an application, E-unitary covers and purecovers for weakly regular *-semigroups are investigated. Furthermore, the spinedproducts of weakly regular *-semigroups are discussed.In the fourth part, we de?ne a relationθon C~*(S), the complete lattice of*-congruences on a weakly regular *-semigroup S, and prove thatθis a congruenceon C~*(S) and each ?*-class is a complete modular sublattice of C~*(S).In the fifth part, we characterize *-congruences on a quasi regular *-semigroups, and we prove that the mapΨ:ρ→Ptrρis a complete lattice morphism of C~*(S)ontoΣ(ρ).