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$k$-Gorenstein Modules

Zhaoyong Huang
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Abstract

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.

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Zhaoyong Huang. 2005-09-07. $k$-Gorenstein Modules. https://arxiv.org/abs/math/0409177

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