κ-Gorenstein Modules

Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext^i （Ext^i （-, U）, U） preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ∧UГwith finite left or right injective dimension.

<Emphasis Type="Italic">k</Emphasis>-Gorenstein Modules

Let Λ and Γ be artin algebras and _Λ U _Γ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to _Λ U _Γ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext ⁱ (Ext ⁱ (−, U), U) preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of _Λ U _Γ with finite left or right injective dimension. Research partially supported by Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20030284033, 20060284002) and NSF of Jiangsu Province of China (Grant No. BK2005207)