The Study Of Reversible And Reflexive Properties Over Monoid Crossed Products

The reflexivity and reversibility of rings are one of the most important research topics in ring theory.In recent years,many scholars at home and abroad have systematically studied them.Monoid crossed product is a more general ring structure than that of monoid groups.We study the reversible and reflexive properties on the monoid crossed product.We define two kinds of important rings which are called strongly CM-reversible rings and strongly CM-reflexive rings,and study their properties.Some results on polynomial rings,skew polynomial rings,monoid rings and skew monoid rings are unified and generalized.This article is divided into the following four chapters.In chapter Ⅰ,we introduce the research background and research purpose.In chapter Ⅱ,we introduce the definitions and concepts involved in this research.In chapter Ⅲ,we study the reversible properties of monoid crossed products.In chapter Ⅳ,we study the reflexive properties of monoid crossed products.