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ANALYTIC SPREAD AND INTEGRAL CLOSURE OF INTEGRALLY DECOMPOSABLE MODULES

Part of: Local rings and semilocal rings Singularities Ring extensions and related topics

Published online by Cambridge University Press:  03 November 2020

CARLES BIVIÀ-AUSINA Open the ORCID record for CARLES BIVIÀ-AUSINA [Opens in a new window]  and
JONATHAN MONTAÑO Open the ORCID record for JONATHAN MONTAÑO [Opens in a new window]
CARLES BIVIÀ-AUSINA
Affiliation:
Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València Camí de Vera, s/n, 46022 València [email protected]
JONATHAN MONTAÑO*
Affiliation:
Department of Mathematical Sciences New Mexico State University 1290 Frenger Mall, MSC 3MB/Science Hall 236 Las Cruces, 88003-8001 New MexicoUSA
*
[email protected]
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Abstract

We relate the analytic spread of a module expressed as the direct sum of two submodules with the analytic spread of its components. We also study a class of submodules whose integral closure can be expressed in terms of the integral closure of its row ideals, and therefore can be obtained by means of a simple computer algebra procedure. In particular, we analyze a class of modules, not necessarily of maximal rank, whose integral closure is determined by the family of Newton polyhedra of their row ideals.

MSC classification

Primary: 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)
Secondary: 13H15: Multiplicity theory and related topics 32S05: Local singularities
Type
Article
Information
Nagoya Mathematical Journal , Volume 245 , March 2022 , pp. 166 - 191
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Copyright
© The Authors, 2020. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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Footnotes

Carles Bivià-Ausina was partially supported by MICINN grant PGC2018-094889-B-I00

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