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.
- Cohen-Macaulay approximations
- Cohen-Macaulay modules
- Gorenstein ring
ASJC Scopus subject areas
- Applied Mathematics