Gorenstein FCR-projective Modules And GP-projective Modules

We introduce and study several new classes of module over a ring R,and provide their characteristic and properties. These extend some classical results.In the first part, a left R-module M is said to be FCR-projective if Ext1(M, A)= 0 for every finitely corelated left R-module A. Then we introduce and inves-tigate Gorenstein FCR-projective modules based on FCR-projective modules. Some properties of Gorenstein FCR-projective modules are obtained in terms of co-noetherian or co-coherent. We also introduce notions of strongly Goren-stein FCR-projective modules and n-strongly Gorenstein FCR-projective mod-ules and discuss their properties.In the second part, a left R-module M is called GP-projective if ExtR1(M, N)= 0 for any Gorenstein projective left R-module N. We discuss some properties of CP-projective modules. Then we character some properties of module when it has finite SGP-projective dimensions.