Generalizations Of Morphic Algebra And Morphic Modules

In recent years,research on morphic extending continuously in the abstract algebra.The research is based on the morphic ring and the morphic module.With the deepening of the research,more and more scholars are interested in the study of the morphic algebra.In 2010 Mao-quan Chu and Guirong Lu have gave the morphic algebra definition and researched it in the literature[13].On the basis of this article,we spreading the morphic algebra and morphic module.This paper is introducing the concept of quasi-morphic algebra,pseudo-morphic algebra,and generalized morphic algebra.At the same time,the pseudo-morphic module and generalized pseudo morphic module are further studied,and some new results are obtained.The second chapter mainly discusses the promotion about morphic algebra,section 2.1 first proposed the concept of quasi-morphic algebra,and gives the relationship between quasi-morphic algebra and regular ring,then discusses the quasi-morphic algebra straight.In the later,the definition of the P-quasi-morphic algebra is given and the nature of it is studied;In section 2.2,the concept of pseudo-morphic algebras is presented,and its properties and determination conditions are discussed.It as well as the relationship between and P-inner ring,right complete ring and P-flat module.Section 2.3 gives the concept of generalized morphic algebras and studies its properties.The third chapter mainly discusses the promotion of morphic module.Section 3.1 introduces the definition,nature and determination conditions of the quasi-morphic module,and gives corresponding examples.Section 3.2 introduces the definition,nature and determination conditions of pseudo-morphic modules.