The Structure And Homomorphism Of Some (W) LR - Regular Pure Groups And Semigroups

As a generalization of the theories of groups and rings, the theory of algebric semigroups has developed as a systematic algebric branch. Regular semigroups are the main study objects of the theory of algebric semigroups. The class of completely regular semigroups is one of the important classes of regular semigroups, since this class of semigroups has more relation with the structures of groups. So it’s also called union of groups. The classes of orthogroups and cryptgroups are two important subclasses of completely regular semigroups, and they are main research objects of the study of completely regular semigroups.In this thesis, we consider the properties and structure representations of the class of (W)LR-normal orthorgroups by the subdirect product, strong semilattice and other methods. And then we discuss the homomorphisms of the class of (W)LR-regular bands by the refined semilattice. Some characterizations and properties of them are given. We also discuss the homomorphisms of the class of (W)LR-normal orthorgroups by the strong semilattice. At last, using the properties and structure representations of them and combining the Yamada Theorem of the class of regular orthorgroups, we get the spined product of (W)LR-regular orthorgroups over Y.There are three chapters in this thesis.In the first chapter, we give some preparations.The structure representations and homomorphisms of (W)LR-normal orthorgroups are con-sidered in the second chapter.We discuss the structure representations of (W)LR-regular orthorgroups by Yamada Theorem in the last chapter.