Study Of Strictly π-Regular Semigroups

In this paper, the properties of strictlyπ-regular semigroups are studied, includ-ing: localization, congruence, ideal and sub-semigroup. In chapter 1, we illustratethe background of semigroups'development and the research status of strictlyπ-regular semigroups. In chapter 2, the strictlyπ-regular semigroups with the greatesthomomorphism image of group are described and the least group congruence by thelocalized concept is given. The aim of chapter 3 is to studyπ-group congruenceof strictlyπ-regular semigroups, and give its ordinary group congruence. Finally,the group congruence of E-idealπ-regular semigroups are investigated. Chapter4 is devoted to investigate various special sub-semigroups, and sub-direct productare studied. Furthermore, we obtain the completely regularity of strictlyπ-regularsemigroups is a hereditary property concerning all the kind of ideals.