Research On Gorenstein FP_n-projective Modes

In this thesis,wemainlyinvestigate the homological properties of FPn-projective modules.The thesis is divided into four chapters.The first chapter gives some preliminaries which are needed in the thesis.In the second chapter,we introduce the notions of FPn-projective modules and FPn-projective dimension of modules,some basic properties of them are given.In particular,we present some new characterizations of ncoherent rings in terms of the FPn-projective modules.Then it isshown that FPnprojective dimension of a module over n-coherent rings situate between FP-projective dimension and finitely presented dimension.We also characterize the rings whose global FPn-projective dimension is zero by using FPn-projective modules.In the third chapter,weintroduce the concept of Gorenstein FPn-projective modulesand give some basic properties of the class of module.Then we discuss the relationship between the Gorenstein FPn-projective modules and some known classesof modules.After clarifying that the class of Gorenstein FPn-projective modules is closed under direct sums and closed under direct summands,we prove that the class of Gorenstein FPn-projective modules is projectively resolving.Further,the stability of Gorenstein FPn-projective modules is also discussed.In the fourth chapter,wesummarize the main work of this thesis,and then point out the direction of the future research on this subject.