Ratliff-Rush Closures and Coefficient Modules

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Abstract

Let (R,m) be ad-dimensional Noetherian local domain. SupposeMis a finitely generated torsion-freeR-module and supposeFis a freeR-module containingM. In analogy with a result of Ratliff and Rush [Indiana Univ. Math. J.27(1978), 929-934] concerning ideals, we define and prove existence and uniqueness of theRatliff-RushclosureofMinF. We also discuss properties of Ratliff-Rush closure. In addition to the preceding assumptions, supposeF/Mhas finite length as anR-module. Then we define theBuchsbaum-RimpolynomialofMinF. In analogy with the work of K. Shah [Trans. Amer. Math. Soc.327(1991), 373-384], we definecoefficientmodulesofMinF. Under the assumption thatRis quasi-unmixed, we prove existence and uniqueness of coefficient modules ofMinF.

Original languageEnglish
Pages (from-to)584-603
Number of pages20
JournalJournal of Algebra
Volume201
Issue number2
DOIs
Publication statusPublished - 1998 Mar 15

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Keywords

  • Buchsbaum-Rim multiplicity
  • Coefficient ideal
  • Hilbert polynomial
  • Integral closure
  • Ratliff-Rush closure
  • Reduction of a module
  • Reduction of an ideal
  • Torsion-free symmetric algebra

ASJC Scopus subject areas

  • Algebra and Number Theory

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