Necessary and sufficient conditions for the Cohen-Macaulayness of form rings
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the Cohen-Macaulayness of form rings
zbMATH Open document ID: 0930.13003
author: Eero Hyry
published in: Journal of Algebra
publication date: 1999-06-17T00:00:00Z
review text: Huckaba and Huneke studied the Cohen-Macaulayness of the graded ring associated to an ideal \(I\) of a Cohen-Macaulay local ring \(A\) under the assumption that \(\text{depth}(A/I^n)\) is big enough [cf. \textit{S. Huckaba} and \textit{C. Huneke}, Am. J. Math. Soc. 114, No. 2, 367-403 (1992; Zbl 0758.13001)]. The question was studied also by others authors (see the references in the paper under review). The purpose of this paper is to give a necessary and sufficient condition for this property, in the same assumptions. One shows also how the depth of the graded ring is related to the vanishing of components of the graded local cohomology.
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 1271642
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: graded ring
zbMATH Keywords: Cohen-Macaulayness of form rings
zbMATH Keywords: depth
zbMATH Keywords: graded local cohomology
reviewed by: Nicolae Manolache
MaRDI profile type: Publication
full work available at URL: jabr.1998.7615
OpenAlex ID: W1994271142
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DOI: 10.1006/JABR.1998.7615
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description: scientific article; zbMATH DE number 1271642