The Regular Semi-group Cross-section Study And Superabundant Semigroup Structure

The semigroup is to the group one kind of attenuation, only requests the dual operation to satisfy the associative law. semi-group's research rised in the 1960s, In certain aspect semigroup theories are similar to the group theoryand ring theory. The most initial period important achievement mainly gives credit to Rees, Clifford and the Dubreil work. To the 70's, semigroups theory Rapidly develops and enriches, which involves with congruence, structure,varieties and so on, but also has the special magazine << Semigroup Forum >>. This period Clifford, A. H, Preton, M, and Howie, J. B and so on have published many important papers one after another, for example [ 13, 18, 19]. At first mainly draws support to Green relates to study some special semigroups like Cliford semigroups, inverse semigroups, oxthodox semigroups, regular semigroups, complete regular semigroups and so on. Since T. S. Blyth and McFadden in [1] introduced regular semigroups with inverse transversals in 1982, this type of semigroup has attracted much attention (see[1, 3, 6, 27, 28]). Since a transversal of semigroup is a subsemigroup of this semigroup, therefore we may say, this topic mentality is quite good grasps the entire semigroupthrough semigroup's some nature. Thus we achieve the partial assurance whole the goal. Let S be a semigroup, S~0 be a subsemigroup of S, S~0 is said to be an inverse transversal of S if the following conditions are satisfied:|V(x)∩S~0| =1 (?)x∈S.Where V(x) denotes the set of inverses of x∈S. Inverse transversal of regular semigroup is relatively extensive, which includes inverse semigroups, inverse semigroups with the basic rectangular band and separable orthodox semigroup and so on. In the last twenty years the theory of regular semigroup with inverse transversal has already been fully developed. Mcalister and McFadden in [2] gave a structure theorem for rugular semigroups with inverse transversals. Saito in [3] gave a construction of this semigroup under normal circumstances. Blyth and Saito studied regular semigroup with Several special type of inverse transversal.In this thesis, the author mainly studies quasi-ideal orthodox transversals and inverse transversals of regular semigroups. It can be divided into three chapters.Chapter 1, the author studies regular semigroups with quasi-ideal orthodoxtransversals. Section 1 is a brief introduction,some background about transversals, The main results and every part of the main content are introduced.In Section 2, some basic conceptions and preliminaries about regular semigroup with quasi-ideal orthodox transversals are introduced. In Section 3, the main objective in this section is to give a structure theorem for rugular semigroups with quasi-ideal orthodox transversals.In Chapter 2, the author studies regular semigroups with inverse transversals.It contains three sections. In Section 1, some background about transversals,The main results and every part of the main content are introduced. In Section 2, some basic conceptions and preliminaries about regular semigroups with quasi-ideal orthodox transversals are introduced. In Section 3, the main objective in this section is to give a structure theorem for rugular semigroups with inverse transversals.Chapter 3 is devoted to a constructing method for superabundant semigroup.It can be divided into 3 sections. In Section 1, some background about transversals, The main results and every part of the main content are introduced. In Section 2, some basic conceptions and preliminaries about superabundantsemigroup are introduced. In Section 3, the main objective in this section is to give a structure theorem for superabundant semigroup.