Gorenstein AC-homological Modules Over Morita Rings

Let Λ(0,0)be a Morita ring which has zero bimodule homomorphisms.In this thesis,we investigate some properties of F P∞-modules over Λ(0,0)and use it to investigate properties of absolutely clean modules and level modules over Λ(0,0),and prove that the functors TA,TB preserve level modules and the functors HA,HB preserve absolutely clean modules under some conditions.Furthermore,by functors TA and HB preserve Gorenstein AC-projective and injective resolution,we prove that under certain conditions,TA(X)is a Gorenstein AC-projective left Λ(0,0)module if and only if left A-module X is a Gorenstein AC-projective module;HA(X)is a Gorenstein AC-injective left Λ(0,0)-module if and only if left A-module X is a Gorenstein AC-injective module.Finally,we give a method to construct Gorenstein AC-projective left Λ(0,0)-module(X,Y,t(IdM?πX),s(IdN?πY))and Gorenstein AC-injective left Λ(0,0)-module(X,Y,(iY)*,(iX)*t)under certain conditions.