Linearity Defect and Regularity over a Koszul Algebra
| dc.creator | Yanagawa, Kohji | |
| dc.date | 2007-07-08 | |
| dc.date | 2007-11-08 | |
| dc.date.accessioned | 2026-07-07T08:41:12Z | |
| dc.date.available | 2026-07-07T08:41:12Z | |
| dc.description | Let A be a Koszul algebra, and $mod A$ the category of finitely generated graded left A-modules. The "linearity defect" ld_A(M) of $M \in mod A$ is an invariant defined by Herzog and Iyengar. An exterior algebra E is a Koszul algebra which is the Koszul dual S^! of a polynomial ring S. Eisenbud et al. showed that $ld_E(M) < \infty$ for all $M \in mod E$. Improving their result, we show the following (and many other facts): (*) If A is a Koszul complete intersection, then $reg_{A^!} (M) < \infty$ and $ld_{A^!} (M) < \infty$ for all $M \in mod A^!$. (**) There is a uniform bound of $ld(J)$, where J is a graded ideal of E. | |
| dc.description | 13 pages. Several proofs have been simplified, and comments on known results have been revised | |
| dc.identifier | https://arxiv.org/abs/0707.1134 | |
| dc.identifier | http://arxiv.org/abs/0707.1134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141609 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.title | Linearity Defect and Regularity over a Koszul Algebra | |
| dc.type | text |