Gorenstein Flat And Injective Modules

Gorenstein projective,injective and flat modules are extension of the classical projec-tive,injective and flat modules,they have the properties that are similar to classical modules, so they play important roles in the study of commutative algebra and homological algebra. E.Enochs and so on defined and studied the Gorenstein modules over Gorenstein rings, then many people study them over Noether rings in the same way of studing classical modules. This artical will continus to study the relation between Gorenstein flat modules and Goren-stein injective modules, and describe n-Gorenstein rings,IF rings with the Gorenstein flat modules. The completion and localization of rings have been studied well,the artical will study Gorenstein flat and Gorenstein injective modules over the completion and localization of rings.