J-Multiplicity and depth of associated graded modules

Claudia Polini, Yu Xie

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let R be a Noetherian local ring. We define the minimal j-multiplicity and almost minimal j-multiplicity of an arbitrary R-ideal on any finite R-module. For any ideal I with minimal j-multiplicity or almost minimal j-multiplicity on a Cohen-Macaulay module M, we prove that under some residual conditions, the associated graded module grI(M) is Cohen-Macaulay or almost Cohen-Macaulay, respectively. Our work generalizes the results for minimal multiplicity and almost minimal multiplicity obtained by Sally, Rossi, Valla, Wang, Huckaba, Elias, Corso, Polini, and Vaz Pinto.

Original languageEnglish (US)
Pages (from-to)31-49
Number of pages19
JournalJournal of Algebra
Volume379
DOIs
StatePublished - Apr 1 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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