Reduction number one for finitely generated torsion-free modules

Research output: Contribution to journalArticle

Abstract

Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. Key words and phrases. integral closure, reduction of an ideal, reduction of a module, reduction number, Rees algebra.

Original languageEnglish
Pages (from-to)3823-3831
Number of pages9
JournalCommunications in Algebra
Volume27
Issue number8
DOIs
Publication statusPublished - 1999 Jan 1

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Reduction number
Torsion-free
Finitely Generated
Module
Rees Algebra
Regular Local Ring
Integral Closure
Exception
Resolve
Unit

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Reduction number one for finitely generated torsion-free modules. / Liu, Jung Chen.

In: Communications in Algebra, Vol. 27, No. 8, 01.01.1999, p. 3823-3831.

Research output: Contribution to journalArticle

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