(Strongly) Gorenstein FP-Projective Modules

As a generalization of FP-injective modules,Gao and Wang introduced the notion of Gorenstein FP-injective modules,and some properties of Gorenstein FP-injective modules were studied.Motivated by their work,as a generalization of FP-projective modules,we introduce and study Gorenstein FP-projective modules and n-strongly Gorenstein FP-projective modules in this dissertation.The dissertation is mainly composed of three sections.Firstly,we introduce the concept of Gorenstein FP-projective modules and present some properties and equivalent characterizations of the class of these mod-ules.The relations between Gorenstein FP-projective modules and related modules are discussed.Then several classes of rings are characterized in terms of Gorenstein FP-projective modules.And the stability of Gorenstein FP-projective modules is studied in this section.Secondly,the notion of Gorenstein FP-projective dimension of modules is in-troduced.An equivalent characterization of Gorenstein FP-projective dimension of modules is given.The relation between FP-projective syzygy of a module and Gorenstein FP-projective syzygy of a module is studied.Finally,we introduce the concept of n-strongly Gorenstein FP-projective mod-ules.Some properties and equivalent characterizations of these modules are given.The relations between n-strongly Gorenstein FP-projective modules and related modules are discussed.