$k$-Gorenstein Modules

Details $k$-Gorenstein Modules $k$-Gorenstein Modules

2004-09-10

arxiv.org/abs/math/0409177v2

Mathematics

Rings and Algebras

18 pages. The statement of Lemma 3.2 is strengthened and the corresponding proof is changed. To appear in Acta Mathematica Sin

Scientific paper

Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ 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 $_{\Lambda}U_{\Gamma}$ with finite left or right injective dimension.

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