Some Studies Of Several Special Semigroups

This dissertation consists of four chapters. In Chapter 1, the development background of semigroups are studied, the important roles of the theory of semigroups in the process of algebra and the progress related to right(left)Ï€-regular, subsemigroups lattice, the theories of congruences are illustrated. In Chapter 2, the equivalent conditions of right(left)Ï€-regular semigroups are given, and the right(left) normal semigroups and completely right(left) normal semigroup are defined, and their equivalent conditions are described. In Chapter 3, we give some properties of epigroup,and we do some researches when subepigroups are lower semidistributive lattices.In Chapter 4, a group congruence on inverse semigroups is defined by a normal subsemigroup of inverse semigroups S, and the maximum(minimum) group congruences are obtained.