N-Strongly Gorenstein Injective Module And Its Generalizations

Projective, injective and flat modules play important roles in homolog-ical algebra, as generalizations of these classical modules,Gorenstein homo-logical modules are widely investigated by many scholars and researchers.In this thesis, n-strongly Gorenstein injective modules and its generalizations are discussed. Most of results are well known.This thesis is divided into four parts:In the first chapter, we introduce some backgrounds of Gorenstein homol-ogy theory and our main work.In chapter2, we introduce the definition of the n-strongly Gorenstein homological module and obtain some related properties. Meanwhile, we get some equivalent conditions of a module is a n-strongly Gorenstein injective (resp. flat) module.In the third chapter, as a generalization of n-strongly Gorenstein injective module, n-strongly Gorenstein FP-injective module is studied. We prove that every n-strongly Gorenstein injective module is n-strongly Gorenstein FP-injective and they are equivalence when R is Gorenstein.In chapter4, we introduce the notion of n-strongly Gorenstein injective complex, some propreties are obtained and we get that every term of a n-strongly Gorenstein injective complex is n-strongly Gorenstein injective mod-ule.