N-Gorenstein Projective Modules Over Morita Context Rings

Let A and B be two associative rings with identities,M a B-A-bimodule,N an A-B-bimodule,and(?)Morita context ring.We write Mod(A(φ,ψ)for the category of left Δ(φ,ψ)-modules.First,we study the n-Gorenstein projective modules over triangular matrix(?).Under some mild conditions,we show that(?)is a n-Gorenstein projective left T-module if and only if M1 is a n-Gorenstein projective left A-module M2/Im φM is a n-Gorenstein projective left B-module and φM is a monomorphism.Next,we study the n-Gorenstein projective modules over Morita context rings Δ(0,0).We show that the functors TA:Mod(A)→ Mod(Δ(0,0))and TB:Mod(B)→Mod(Δ(0,0))preserve n-Gorenstein projective modules if the bimodules M and N satisfy some mild conditions.Inspired by the work of Gao and Psaroudakis in[6],we give a method of constructing n-Gorenstein projective Λ(0,0)-modules.As an application of this result,we get some conclusions and examples over special Morita context rings(?)where R be a ring.Finally,in the case of Gorenstein algebras,we further study the n-Gorenstein projective modules over Morita context ring.