On the higher delta invariants of a Gorenstein local ring

Yuji Yoshino

On the higher delta invariants of a Gorenstein local ring

Research output: Contribution to journal › Article

Abstract

Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δ_Rⁿ(M) for each module M and for each integer n. We propose a conjecture asking if δ_Rⁿ(R/m^ℓ) = 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 δ_Rⁿ(R/m^ℓ) > 0.

Original language	English
Pages (from-to)	2641-2647
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	124
Issue number	9
Publication status	Published - Dec 1 1996
Externally published	Yes

Keywords

Cohen-Macaulay approximations
Cohen-Macaulay modules
Gorenstein ring

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Cite this

Yoshino, Y. (1996). On the higher delta invariants of a Gorenstein local ring. Proceedings of the American Mathematical Society, 124(9), 2641-2647.

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