?-gorenstein Projective Dimension And Tate Cohomology

In this thesis,we study ?-Gorenstein projective dimension for modules and complexes,respectively,and Tate cohomology of complexes,where ? is a class of R-modules that contains all projective R-modules.Firstly,we give some charac-terizations of ?-Gorenstein projective dimension of modules,then we discuss the properties of this homology dimension,we prove that every R-modules finite X-Gorenstein projective dimension admits a proper ?-Gorenstein projective resolu-tion.Secondly,we introduce the notion of complete ?-resolutions for complexes,then we use this notion to define the ?-Gorenstein projective dimension of complexes,some characterizations of ?-Gorenstein projective dimension of complexes is then given.Fi-nally,the Tate cohomology of complexes relative to complete ?-resolutions is in-vestigated,and the balancedness of this generalized Tate cohomology is also consid-ered.Our results unify and generalized the related researches.