Abstract
Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δRn(M) for each module M and for each integer n. We propose a conjecture asking if δRn(R/mℓ) = 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 δRn(R/mℓ) > 0.
Original language | English |
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Pages (from-to) | 2641-2647 |
Number of pages | 7 |
Journal | Proceedings of the American Mathematical Society |
Volume | 124 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1996 |
Externally published | Yes |
Keywords
- Cohen-Macaulay approximations
- Cohen-Macaulay modules
- Gorenstein ring
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics