k-Gorenstein Modules

2004/09/10 by Zhaoyong Huang, Huang, Zhaoyong
Mathematics · #16E10 #16E30 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16E10 #msc:16E30

paper · pdf · doi:10.48550/arxiv.math/0409177

18 pages. The statement of Lemma 3.2 is strengthened and the corresponding proof is changed. To appear in Acta Mathematica Sinica (English Series)

arxiv created 2005/09/07 · arxiv updated 2009/12/01

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 Extⁱ(\rm Extⁱ(-, 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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