Algebras that satisfy Auslander's condition on vanishing of cohomology
| dc.creator | Christensen, Lars Winther | |
| dc.creator | Holm, Henrik | |
| dc.date | 2008-01-02 | |
| dc.date | 2009-01-21 | |
| dc.date.accessioned | 2026-07-07T12:31:44Z | |
| dc.date.available | 2026-07-07T12:31:44Z | |
| dc.description | Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of cohomology of finitely generated modules. The failure of this conjecture - by a 2003 counterexample due to Jorgensen and Sega - motivates the consideration of the class of rings that do satisfy Auslander's condition. We call them AC rings and show that an AC Artin algebra that is left-Gorenstein is also right-Gorenstein. Furthermore, the Auslander-Reiten Conjecture is proved for AC rings, and Auslander's G-dimension is shown to be functorial for AC rings that are commutative or have a dualizing complex. | |
| dc.description | Final version, to appear in Math. Z. 20 pp | |
| dc.identifier | https://arxiv.org/abs/0801.0401 | |
| dc.identifier | http://arxiv.org/abs/0801.0401 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216545 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | 16E65; 16E30; 13D05 | |
| dc.title | Algebras that satisfy Auslander's condition on vanishing of cohomology | |
| dc.type | text |