Bounds for the number of generators of generalized Cohen-Macaulay ideals
type: Item
instance of: scholarly article
title: Bounds for the number of generators of generalized Cohen-Macaulay ideals
zbMATH Open document ID: 0846.13009
author: Le Tuan Hoa
published in: Journal of Algebra
publication date: 1996-09-22T00:00:00Z
review text: Let \((S,M)\) be a Cohen-Macaulay local ring and \(I\) an ideal. The author deals with the problem of finding the number of generators for such ideals. Numerically this number will depend on properties of \(R = S/I\). For example one may try to find bounds depending on \(e(R)\), the multiplicity of \(R\). Of course this is still hopeless. Earlier papers and books dealt with this problem with more restrictions on \(I\), like Cohen-Macaulay property for \(R\). Here the author deals with the problem when \(I\) is a generalized Cohen-Macaulay ideal. That is to say, the local cohomology modules \(H^i_M (R)\) are of finite length for all \(i < \dim R\). \textit{Ngô Viêt Trung} and others proved bounds for the number of generators for \(I\) as above which depend on the length of these local cohomology modules. Here the author proves estimates for these numbers which depend on a much cruder number \(l\), where one only needs that \(M^l\) is an \(R\)-standard ideal and such an \(l\) exists if \(R\) is a generalized Cohen-Macaulay ring.
reviewed by: N. Mohan Kumar
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 826752
zbMATH Keywords: Cohen-Macaulay local ring
zbMATH Keywords: number of generators
zbMATH Keywords: local cohomology
MaRDI profile type: Publication
full work available at URL: jabr.1995.1351
OpenAlex ID: W2011512356
DOI: 10.1006/JABR.1995.1351
description: scientific article; zbMATH DE number 826752