$k$-Gorenstein Modules
| dc.creator | Huang, Zhaoyong | |
| dc.date | 2004-09-10 | |
| dc.date | 2005-09-07 | |
| dc.date.accessioned | 2026-07-07T05:12:01Z | |
| dc.date.available | 2026-07-07T05:12:01Z | |
| dc.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. | |
| dc.description | 18 pages. The statement of Lemma 3.2 is strengthened and the corresponding proof is changed. To appear in Acta Mathematica Sinica (English Series) | |
| dc.identifier | https://arxiv.org/abs/math/0409177 | |
| dc.identifier | http://arxiv.org/abs/math/0409177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72439 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.subject | 16E10; 16E30 | |
| dc.title | $k$-Gorenstein Modules | |
| dc.type | text |