Some Studies On Generalized Regular Semigroups

Regular semigroups in studying of theory of semigroups have been mainly topics. In the recent years, many authors generalized the usual Green's relations to different forms in order to obtain some generalized regular semigroups, for example, abundant semigroups, rpp semigroups and quasi-regular semigroups. These class of semigroups have attracted more and more attention.It is well known that an important aim of studying semigroups is to investigate its structure of this class of semigroups.This paper is divided into four chapters. In the first part, we give some definitions and properties of semigroups which are useful in the later chapters. In the second part, we establish the construction for super R~*-unipotent semigroups by generalized left △-product. This structure studies this kinds of semigroups from another view point. In the third part, we use the concept of right △-product to investigate the right C — rpp semigroups whose idempotents form a right normal band. Also we prove that it is a strong semilattice of direct product of left cancellative monoids and right zero bands. In the last chapter, we first introduce the (?) relations. Then we define the relation 7 on the adequate Ε-right quasi-wrpp semigroups. Finally, by the relation 7, we mainly discuss a kind of quasi-wrpp semigroups, so-called perfect right quasi-wrpp semigroups and obtain some properties and structure for these semigroups. In particular, our result on perfect right quasi-wrpp semigroups is a generalization of theorem obtained by Peng's in[36].