The a-invariant and gorensteinness of graded rings associated to filtrations of ideals in regular local rings

Shiro Goto, Futoshi Hayasaka, Shin Ichiro Iai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let A be a regular local ring and let ℱ = {Fn}n∈Zdbl; be a filtration of ideals in A such that ℛ(ℱ) = ⊕n≥0 Fn is a Noetherian ring with dim ℛ(ℱ) dim A + 1. Let script G sign (ℱ) = ⊕n≥0 Fn/Fn+1 and let a(script G sign(ℱ)) be the a-invariant of script G sign(ℱ). Then the theorem says that F1 is a principal ideal and Fn = F1n for all n ∈ Zdbl; if and only if script G sign (ℱ) is a Gorenstein ring and a script G sign(ℱ)) = -1. Hence a script G sign(ℱ)) ≤ -2, if script G sign (ℱ) is a Gorenstein ring, but the ideal F1 is not principal.

Original languageEnglish
Pages (from-to)87-94
Number of pages8
JournalProceedings of the American Mathematical Society
Volume131
Issue number1
DOIs
Publication statusPublished - Jan 1 2003
Externally publishedYes

Keywords

  • Associated graded ring
  • Filtration of ideals
  • Gorenstein local ring
  • Injective dimension
  • Integrally closed ideal
  • Rees algebra
  • Regular local ring
  • a-invariant
  • m-full ideal

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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