Properties And Application Of ～#-abundant Semigroups

In this thesis, we mainly study #-abundant semigroups. It can be divided into four chapters.In the first Chapter, there is a brief introduction. The basic concepts, necessary preliminaries and it's developing background are given.In the second Chapter, we study some properties about Green's—- relations. It contains two sections. In Section 1, some basic concepts and preliminaries about #-abundant semigroups are introduced, they are necessarily prepared to study Green's—- relations. In Section 2, we generalize the relative results of Green's *- relations, and get some properties about #-abundant semigroups.In the third Chapter, we study the natural partial order≤on #-abundant semigroups. It gives another equivalent characterize by idempotent elements.In the fourth Chapter, we study strongly E-#-abundant semigroups. It contains three sections. In Section 1, we introduce perfect right #-abundant semigroup, we investigate the structure of perfect right #-abundant semigroups, and give some equivalent characterizes. In Section 2, congruence relations on strongly E-#-abundant semigroups are introduced, the three biggest congruence relations contained in L,R,H are given, many equivalent characterizes are given by the three congruence relations. Finally, we characterize the properties of strongly E-#-abundant semigroups by E. In Section 3, the translational hull of strongly E-#-abundant semigroups. By two defined relations, we obtain that the translational hull of strongly E-#-abundant semigroups is strongly E-#-abundant semigroups.