Reduction number one for finitely generated torsion-free modules

研究成果: 雜誌貢獻文章


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.

頁(從 - 到)3823-3831
期刊Communications in Algebra
出版狀態已發佈 - 1999 一月 1

ASJC Scopus subject areas

  • Algebra and Number Theory

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