Structures Of Some Geeneralized Regular Semigroups

In this dissertation, we study the structures of some generalized regular semigroups. The main idea is to describe structures of the generalized regular semigroups by generalized Green relations and in terms of the structures of the set of some idempotents in generalized semigroups.Regular semigroups, particularly complete regular semigroups are a class of very important semigroups. The structure of some orthodox complete regular semigroups have been discribed. In this paper, the structure will be generalied to the according to some generalized regular semigroups. There are three chapters.In the first chapter, we deal with LR-(7-Ehresmann semigroups and LR-normal-Ehresmann semigroups. We introduce the concept of LR-C-Ehresmann orthogroups which is an analogue of LR- C semigroups in the range of U-semiabundant semigroups. Some structure theorems of such orthogroups are obtained. Related results obtained by Gomes and Gould on C' -Ehresmann semigroups and some results obtained by Guo and Shum on LR-normal orthogroups are amalgamated and generalized. In particular, we will construct a LR-normal C1 -Ehresmann orthogroup by gearing together a left normal C' -Ehresmann orthogroup. a right normal C -Ehresmann orthogroup with respect to a C'-Ehresmann semigroup on a geared semilattice.In the second chapter, we give the description of the structure of left, semiregular-illiberal semigroups. Firstly, we give the definition of left semiregular-W -liberal semigroups, i.e.the orthodox U - liberal semigroups with the set of projections being left semiregular bands. Secondly, we obtain the semi- spined product structure and the A-product structure of left semiregular ?/-liberal semigroups. Thirdly, we give thestructure of left seminormal-?-liberal semigroups through a corollary.In the third chapter, we describe the structures of orthodox U-liberal semigroups and its some special subclasses, then in terms of the structures, we describe the isomorphisms on orthodox U-liberal semigroups. Firstly, we give the semi- spined product structure and the A-product structure of orthodox U-liberal semigroups: A semigroup S is an orthodox U-liberal semigroup if and only if 5 is a semi-spined product (A -product) of the C-Ehresmann semigroup T, the set / and the set A with respect to a semilat-tice y and structual homomorphisms ?and 77. Secondly, we describe the isomorphism on orthodox U-liberal semigroups. Thirdly, we give the structures of its some special subclasses.