Sally modules of m-primary ideals in local rings

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7 Scopus citations

Abstract

Given any local Noetherian ring (R, m), we study invariants, such as the dimension and multiplicity, of the Sally module SJ(I) of any m-primary ideal I with respect to a minimal reduction J. As a by-product we obtain an estimate for the Hilbert coefficients of m that generalizes a bound established by Elias and Valla in a local Cohen-Macaulay setting. We also find sharp estimates for the multiplicity of the special fiber ring F(I) of I, which recover previous bounds established by Polini, Vasconcelos, and the author in the local Cohen-Macaulay case. A particular attention is also paid to Sally modules in local Buchsbaum rings.

Original languageEnglish
Pages (from-to)4503-4515
Number of pages13
JournalCommunications in Algebra
Volume37
Issue number12
DOIs
StatePublished - Dec 2009

Keywords

  • Blow-up algebras
  • Multiplicities

ASJC Scopus subject areas

  • Algebra and Number Theory

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