On the higher delta invariants of a Gorenstein local ring

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Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δR n(M) for each module M and for each integer n. We propose a conjecture asking if δR n(R/m) = 0 for any positive integers n and ℓ. We prove that this is true provided the associated graded ring of R has depth not less than dim R - 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n, ℓ) for which δR n(R/m) > 0.

Original languageEnglish
Pages (from-to)2641-2647
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number9
Publication statusPublished - 1996
Externally publishedYes



  • Cohen-Macaulay approximations
  • Cohen-Macaulay modules
  • Gorenstein ring

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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