$k$-Gorenstein Modules
Abstract
Description
Let $Λ$ and $Γ$ be artin algebras and $_ΛU_Γ$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_ΛU_Γ$ and then characterize it in terms of the $U$-resolution dimension of some special injective modules and the property of the functors ${\rm Ext}^{i}({\rm Ext}^{i}(-, U), U)$ 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 $_ΛU_Γ$ with finite left or right injective dimension.
18 pages. The statement of Lemma 3.2 is strengthened and the corresponding proof is changed. To appear in Acta Mathematica Sinica (English Series)
18 pages. The statement of Lemma 3.2 is strengthened and the corresponding proof is changed. To appear in Acta Mathematica Sinica (English Series)