Reduction number one for finitely generated torsion-free modules

Jung Chen Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Issue number8
Publication statusPublished - 1999
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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