Wrpp Semi-group Study

We investigate wrpp semigroups in this paper. It is divided into seven sections.In the first section and the second section, the basic concepts and necessary preliminaries are given, and the concept of pseudo abundant semigroups is introduced, we illustrate that a class of pseudo abundant semigroups is more extensive than that of abundant semigroups.In the third section, we study some properties of Green's ** relations, which generalize the relative results of Green's * relations, and investigate the properties of some classes of pseudo abundant semigroups.In the fourth section, we characterize the structure of left C-wrpp semigroups in terms of left cross products.In the fifth section, a concept of perfect wrpp semigroups is introduced, and we investigate the structure of perfect wrpp semigroups. We give some equivalent characterization for perfect wrpp semigroups.In the sixth section, a concept of eventually PI strong wrpp is introduced, and we characterize the structure of eventually PI strong wrpp semigroups.In the seventh section, we give the refined semilattice structure of a special class of of left C-wrpp semigroups, which generalize the main results of refined semilattice of left C-rpp semigroups.