On the higher delta invariants of a Gorenstein local ring

Yuji Yoshino

doi:10.1090/s0002-9939-96-03376-x

On the higher delta invariants of a Gorenstein local ring

Yuji Yoshino

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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
DOIs	https://doi.org/10.1090/s0002-9939-96-03376-x
Publication status	Published - 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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keywords = "Cohen-Macaulay approximations, Cohen-Macaulay modules, Gorenstein ring",

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AU - Yoshino, Yuji

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - Cohen-Macaulay approximations

KW - Cohen-Macaulay modules

KW - Gorenstein ring

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EP - 2647

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

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ER -

On the higher delta invariants of a Gorenstein local ring

Abstract

Keywords

ASJC Scopus subject areas

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