Some Studies Of Superflous Flat Semi-modules And Superflous Projective Semi-modules

In the paper,we mainly investigate superfluous injective semi-modules 、superflous flat semi-modules and Superflous projective semi-modules.Discuss the properties of superfluous injective semi-modules 、 superflous flat semi-modules 、Superflous projective semi-modules.The paper falls into four parts.The first section is the preliminaries,we introduce corresponding definitions and conclusions which are be used frequently.The second section,we introduce the concept of superfluous injective semi-modules,some properties of it are given.Moreover,we define superfluous injective cover,and discuss their related properties.The third section,we define superflous flat semi-modules and k-superflous flat semi-modules,and discuss their related properties.Then describe the relationship of k-Superflous flat semi-modules and superflous injective semi-modules.The fourth part,on the basic of semi-modules we introduce the concept of superflous projective semi-modules,and give the superflous projective semi-modules equivalent characterizations,then the Schanuel Lemma of relatively superfous projective semi-modules is proved.