Gorenstein Injective Objects In Comma Categories And Frobenius Bimodules

In this paper,we mainly study Gorenstein injective objects in the right comma category,and discuss relationships between Frobenius bimodules and Gorenstein homological properties.Firstly,we study Gorenstein injective objects in the right comma category.Let A and B be abelian categories,G an additive and left exact functor from B to A,and(G?A) the right comma category.If G is coperfect,then we get equivalent characterizations of Gorenstein injective objects in the right comma category(G?A),and construct recollements induced by Gorenstein injective objects.Secondly,we study relationships between Frobenius bimodules and Gorenstein homological properties.Let S and R be associative rings with an identity,S_M_R a Frobenius bimodule with M_R a generator.We prove that(a)R-module X is n-Gorenstein projective if and only if M(?)_R X is a n-Gorenstein projective-module;(b)If any level-moduleis a direct summand of Hom_S(M,M(?)_R A),then R-module X is Gorenstein AC-projective if and only if M(?)_RX is a Gorenstein AC-projective S-module.