Some Studies On Max-Projective Semimodules

The theory of semi-modules is the promotion of the theory of modules on semi-modules,they are similar in the structures,but the distinctions between them exist at the same time.This paper is mainly about max-projective semi-modules,the characterizations about them are discussed,and we introduce the concepts of proper max-projective decomposition and proper max-projective dimension of semi-modules,then some related results of them are obtained.This paper is divided into three sections:The first section is preliminary.Some definitions and results that may be used are introduced,which are probably used in the paper.In the second section,firstly,we give the definition of max-projective semi-modules.Then the properties of max-projective semi-modules are discussed,on the basis of which the relationship of max-projective semi-modules and functor(7)PHom,-(8)is depicted.After that we get the equivalent characterizations about max-projective semi-modules.Then we introduce the concepts of proper max-projective decomposition and proper max-projective dimension,and meanwhile extend the Schanuel Lemma from projective semi-modules to max-projective semi-modules.Then some conclusions are acquired.The last section is max-injective semi-modules and f-injective semi-modules,we define the max-injective semi-modules at first,then give the test theory of max-injective semi-modules,and some relative properties are also investigated.