A Study On H-abundant Semigroup

In this paper, we mainly study H-abundant semigroups. It can be divided into five chapters.Chapter1is introduction. We give definition of H-abundant semigroups and research backgrounds of this paper. Then, we give an outline of this paper.In chapter2, we introduce some relative concepts of H-abundant semigroups and study some properties of Green-relations. We generalize some relative results of Green#relations, and get some properties of H-abundant semigroups.In chapter3, we investigate natural partial order on H-abundant semigroups. It gives another equivalent characterization in term of idempotents.In chapter4, we study strongly E-H-abundant semigroups. It contains three sec-tions. In section1, the relation δ is defined on strongly E-right～-abundant semigroups, some properties about δ are given. We introduce the concept of perfect right～-abundant semigroups. We investigate the structure of perfect right～-abundant semigroups, and give some equivalent characterizations. In second2, we introduce congruences of strong-ly E-’H-abundant semigroups. We give three biggest congruences contained in (?),R,H respectively, many equivalent characterizations are given by the three congruences. Fi-nally, we characterize some properties of strongly E-H-abundant semigroups in term of idempotents. In section3, we study the translational hull of strongly E-H-abundant semigroups. We obtain that translational hulls of strongly E-H-abundant semigroups are strongly E-H-abundant semigroups.In chapter5, we introduce the concept of super H-abundant semigroups, and give its semilattice decomposition. At the same time, a sufficient and necessary condition for a super H-abundant semigroup to be a normal super H-abundant semigroup is given.