GF_ac-phantom And GI_ac-cophantom Morphisms

In the thesis,we introduce the concepts of GF_ac-phantom and GI_ac-cophantom morphisms,provide some homological properties of GF_ac-phantom and GUac-cophantom morphisms,and show that every morphism left R-modules has a GF_ac-phantom cover.Furthermore,we characterize Gorenstein AC-flat objects and Gorenstein ACinjective objects in H（R）,investigate preservance of n-GF_ac-phantom and n-GI_accophantom morphisms under change of rings,and show that under certain conditions,right S-morphism ψ（?）R1:A（?）RS→B（?）RS is an n-GF_ac-phantom morphism if ψ:AR→B_R is an n-GF_ac-phantom morphism in Mod-R.At last,we introduce GF_ac-Tor_n-epimorphism and GI_ac-Extn-monomorphism,discuss the relationship between higher GF_ac-phantom and GI_ac-cophantom morphisms,and prove that morphism f:M→N in R-Mod is an n-GF_ac-phantom morphism if and only if f is a△ⁿ-phantom morphism.