| By means of sequences of FPn-injective modules and C-FPn-injective modules re-spectively,this paper introduces Gorenstein FPn-injective modules and C-Gorenstein FPn-injective modules.Over n-coherent rings,several important properties of Goren-stein FPn-injective modules and Gorenstein FPn-injective dimensions are obtained,and the stability and Foxby equivalence of C-Gorenstein FPn-injective modules are studied.The organization of this paper is as follows.In the second chapter,we first introduce the concept of FPn-injective dimension,and give some equivalent characterizations of FPn-injective dimension.Then Goren-stein FPn-injective modules are introduced and the concept of GFPnI-closed ring is given.Some closure problems of Gorenstein FPn-injective modules in a short exact sequence and some equivalent characterizations of Gorenstein FPn-injective modules are studied.It is proved that n-coherent rings are GFPnI-closed if and only if Goren-stein FPn-injective modules are injectively coresolving.Furthermore,the concept of Gorenstein FPn-injective dimension is introduced,and the Gorenstein FPn-injective di-mension is characterized.That is,when R is GFPnI-closed and n-coherent,GFPn-idR（M）≤m if and only if,for any integer k（1≤k≤m）,there is an exact sequence0＞M＞G0＞G1＞...＞Gk 1＞Ek＞Ek+1＞Em＞0 such that Gi∈GFPnI when 0≤i<k,and Ej∈FPnI when j>k.Finally,We also define and study Gorenstein FPn-flat modules in a similar way.In the third chapter,we introduce C-Gorenstein FPn-injective modules.WhenSCRis a faithfully semidualizing bimodule and S is an n-coherent ring,it is shown that the C-Gorenstein FPn-injective module is closed under extension,cokernel of monomorphism,direct product and direct summand.It is also obtained that the two-degree C-Gorenstein FPn-injective module is still the C-Gorenstein FPn-injective module.Hence its stability is obtained.Finally,we discuss how to construct the Foxby equivalence of C-Gorenstein FPn-injective module. |
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