Study On Regularity Of Semirings

Semiring theory is an important part of algebra.In many aspects of the theory of semirings,study the regularity and its special situation is one of the hotspots in the field.Semiring theory has been widely used in the form of language,information science and automation theory and other field.In this thesis,we study the regularity of several kinds of special semirings by using the theory and method of semigroups.The thesis is divided into four chapters.The first chapter is an introduction,which briefly introduces the general situation of the development of the theory of semirings at home and abroad,and the research background and significance,and introduces the main research contents and the work of this paper.The second chapter semirings regularity.First introduces the main concepts and results needed in this paper.Then the regularity of semirings,given semiring for regular semiring equivalent characterizations.In the third chapter,we introduce the semi direct product of semirings.By introducing the concept of the product of semirings,we study the regularity of the semidirect product of semirings.In the fourth chapter,we discuss the properties of the semiring product of several kinds of special regular semirings by introducing the concept of semiring cyclic product regularization.