Fpn-mode And ξ-Gorenstein Injective Modules

In this thesis, we investigate two parts as follows:In the first part, we introduce notions of fpn-injective modules and fpn-flat modules base on n-presented modules. Then we discuss some basic properties of fpn-injective module (fpn-flat module) pre-covers and fpn-injective module (fpn-flat module) preenvelopes. We also discuss some properties of fpn-injective modules and fpn-flat modules under (almost) excellent extensions. These results give us generalizations of previous results on fp-injective modules and fp-flat modules.In the second part, we introduce the definition of ζ-Gorenstein injective modules base on a particular class of short exact sequences named a proper class. Then we study theζ-Gorenstein injective dimension and its properties. We also give a notion of strong ζ-Gorenstein injective modules and their properties. These generalize related results on Gorenstein injective modules and strong Gorenstein modules.