On the Gorenstein property of the associated graded ring of a power of an ideal
type: Item
instance of: scholarly article
title: On the Gorenstein property of the associated graded ring of a power of an ideal
zbMATH Open document ID: 0812.13005
DOI: 10.1007/BF03026533
author: Eero Hyry
published in: Manuscripta Mathematica
publication date: 1995-05-14T00:00:00Z
full work available at URL: https://eudml.org/doc/155855
review text: Let \(I\) be an ideal of positive height \(h\) in a local ring \(A\) such that the form ring \(gr_ A (I) = \oplus_{n \geq 0} I^ n/I^{n+1}\) is Cohen-Macaulay. The author proves (theorem 2.4) that, for \(r \geq 1\), the form ring \(gr_ A (I^ r)\) is Gorenstein if and only if \(gr_ A (I)\) is Gorenstein and \(a(gr_ A (I)) \equiv -1\) mod \(r\), where \(a(gr_ A(I))\) denotes the \(a\)-invariant of the graded ring \(gr_ A(I)\). That was known before only when \(h\geq 2\) [cf. \textit{M. Herrmann}, \textit{J. Ribbe} and \textit{P. Schenzel}, Math. Z. 213, No. 2, 301-309 (1993; Zbl 0797.13001)]; the author provides a proof which works for all \(h \geq 1\).
reviewed by: Jürgen Ribbe
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 492803
zbMATH Keywords: \(a\)-invariant
zbMATH Keywords: Gorensteinness
zbMATH Keywords: local ring
zbMATH Keywords: form ring
MaRDI profile type: Publication
cites work: The Cohen-Macaulay symbolic Rees algebras for curve singularities
cites work: On graded rings. I
cites work: On graded rings. II: \(\mathbb{Z}\)-graded rings
cites work: Q4040095
cites work: On the Gorenstein property of form rings
cites work: On the Gorenstein property of the associated graded ring and the Rees algebra of an ideal
cites work: Q4002995
cites work: When is the rees algebra cohen—macaulay?
description: scientific article; zbMATH DE number 492803