A numerical characterization of reduction for arbitrary modules
| dc.creator | Callejas-Bedregal, R. | |
| dc.creator | Perez, V. H. Jorge | |
| dc.date | 2006-11-27 | |
| dc.date | 2007-02-09 | |
| dc.date.accessioned | 2026-07-07T07:45:35Z | |
| dc.date.available | 2026-07-07T07:45:35Z | |
| dc.description | Let $(R, \mathfrak m)$ be a $d$-dimensional Noetherian local ring and $E$ a finitely generated $R$-submodule of a free module $R^p.$ In this work we introduce a multiplicity sequence $c_k(E), k=0,..., d+p-1$ for $E$ that generalize the Buchsbaum-Rim multiplicity defined when $E$ has finite colength in $R^p$ as well as the Achilles-Manaresi multiplicity sequence that applies when $E\subseteq R$ is an ideal. Our main result is that the new multiplicity sequence can indeed be used to detect integral dependence of modules. Our proof is self-contained and implies known numerical criteria for integral dependence of ideals and modules. | |
| dc.description | 30 pages.Completely revised version | |
| dc.identifier | https://arxiv.org/abs/math/0611834 | |
| dc.identifier | http://arxiv.org/abs/math/0611834 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123573 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13H15(primary) 13B22(secondary) | |
| dc.title | A numerical characterization of reduction for arbitrary modules | |
| dc.type | text |