A numerical characterization of reduction for arbitrary modules

dc.creatorCallejas-Bedregal, R.
dc.creatorPerez, V. H. Jorge
dc.date2006-11-27
dc.date2007-02-09
dc.date.accessioned2026-07-07T07:45:35Z
dc.date.available2026-07-07T07:45:35Z
dc.descriptionLet $(R, \mathfrak m)$ 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.description30 pages.Completely revised version
dc.identifierhttps://arxiv.org/abs/math/0611834
dc.identifierhttp://arxiv.org/abs/math/0611834
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123573
dc.subjectCommutative Algebra
dc.subject13H15(primary) 13B22(secondary)
dc.titleA numerical characterization of reduction for arbitrary modules
dc.typetext

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