Some Studies Of Quasi-Essential Injective Semi-Modules And Essential Flat Semi-Modules

In the paper, we mainly investigate quasi-essential injective semi-modules and essential flat semi-modules. Discuss the properties of quasi-essential injective semi-modules, the results of essential flat semi-modules and k-essential flat semi-modules. Describe the relationship of k-essential flat semi-modules and essential injective 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.In the second section, we introduce the concept of quasi-essential injective semi-modules, and we gain the equivalent characters of quasi-essential injective semi-modules. Describe the relationship of quasi-essential injective semi-modules E and HomR(-, E). Moreover, we define quasi-essential injective cover, and discuss their related properties.In the third section, on the basis of exact sequence and tensor product, we introduce the concept of essential flat semi-modules and k-essential flat semi-modules. Moreover, discuss the relationship of k-essential flat semi-modules and essential injective semi-modules.In the fourth section, we define essential projective semi-modules, and discuss their related properties.