Some Studies On Weakly P-inversive Semigroups

In this paper, we study weakly P-inversive semigroups. It is composed offour chapters.Chapter1is a brief introduction and the basic concepts and necessary prelim-inaries. We introduce concepts of weakly P-inversive semigroups and the strongP-congruences.In chapter2, we prove that the lattice of strong P-congruences is a completesublattice of the lattice of congruences. At the same time, the least element of thelattice of strong P-congruences is given. Furthermore, we discuss the relationsbetween strong P-congruences on weakly P-inversive semigroups and regular-semigroups.In chapter3, we introduce concepts of strong normal partition, strong nor-mal equivalence and the concept of characteristic trace of strong P-congruenceson P-inversive semigroups. By using them, we study the properties of the latticesof strong P-congruences, such as the greatest element respect to having strongnormal equivalence as its C-trace, relation θ determined by strong normal equiv-alence is a congruence on lattices of strong P-congruences and each θ-class is acomplete sublattice of lattices of strong P-congruences and so on.In chapter4, we give the construction of all P-subdirect products of weaklyP-inversive semigroups and we introduce the concepts of E-unitary weakly P-inversive covers of weakly P-inversive semigroups and study the unitary P-subho-momorphisms of weakly P-inversive semigroups onto groups.