Non-commutative Castelnuovo-Mumford Regularity and AS-regular Algebras
| dc.creator | Dong, Z. -C. | |
| dc.creator | Wu, Q. -S. | |
| dc.date | 2008-08-04 | |
| dc.date.accessioned | 2026-07-07T09:54:33Z | |
| dc.date.available | 2026-07-07T09:54:33Z | |
| dc.description | Let $A$ be a connected graded $k$-algebra with a balanced dualizing complex. We prove that $A$ is a Koszul AS-regular algebra if and only if that the Castelnuovo-Mumford regularity and the Ext-regularity coincide for all finitely generated $A$-modules. This can be viewed as a non-commutative version of \cite[Theorem 1.3]{ro}. By using Castelnuovo-Mumford regularity, we prove that any Koszul standard AS-Gorenstein algebra is AS-regular. As a preparation to prove the main result, we also prove the following statements are equivalent: (1) $A$ is AS-Gorenstein; (2) $A$ has finite left injective dimension; (3) the dualizing complex has finite left projective dimension. This generalizes \cite[Corollary 5.9]{mori}. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0808.0407 | |
| dc.identifier | http://arxiv.org/abs/0808.0407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166352 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 16W50, 16E30, 16E65, 14A22 | |
| dc.title | Non-commutative Castelnuovo-Mumford Regularity and AS-regular Algebras | |
| dc.type | text |