On Some Classes Of Completely Regular Semirings

In this thesis, we devote to study two important classes of semirings, in which the additive reducts of semirings are normal orthogroups or rectangular groups. We diliberate the fundamental properties and structure of semirings in the two classes. At the same time, we investigate the sturdy frames of M-completely regular semirings.This thesis consists of four chapters. The first chapter includes the basic notations and definitons. We introduce some concepts and theories related to semirings, and recall the notations and results of completely regular semigroups which will be used in the following. In chapter two, we consider a semiring class in which the additive reducts of semirings are rectangular group. We characterize the properties and obtain the decomposition of subdirect products of members in this class. In chapter three, we investigate the semirings whose additive reducts are normal orthogroups. We extend a few of congruences in completely regular semigroups to semirings. From different ways, we give the decompositions of subdirect products and Mal'cev products of these semirings by making using of the extended congruences. In chapter four, we investigate the sturdy frames of M-completely regular semirings.