Asymptotic stability of primes associated to homogeneous components of multigraded modules

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Abstract

Let A ⊆ B be a homogeneous extension of Noetherian standard Nr-graded rings with A0 = B0 = R. Let M be a finitely generated Nr-graded B-module and N ⊆ M a finitely generated graded A-submodule of M. In this paper, we investigate the asymptotic behavior of the set of primes associated to the module Mn / Nn and prove that for all sufficiently large n ∈ Nr, the set AssR (Mn / Nn) is stable. We also give a certain inequality for the spread of standard multigraded rings, which is a natural generalization of Burch's inequality for the analytic spread of an ideal.

Original languageEnglish
Pages (from-to)535-543
Number of pages9
JournalJournal of Algebra
Volume306
Issue number2
DOIs
Publication statusPublished - Dec 15 2006

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Keywords

  • Associated prime
  • Grade
  • Multigraded
  • Spread

ASJC Scopus subject areas

  • Algebra and Number Theory

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