Primary decompositions of three-generated ideals
type: Item
instance of: scholarly article
title: Primary decompositions of three-generated ideals
zbMATH Open document ID: 0843.13001
DOI: 10.1016/0022-4049(94)00143-X
author: Chun-Tak Fan
published in: Journal of Pure and Applied Algebra
publication date: 1996-08-18T00:00:00Z
review text: Let \(R\) be a three-generated height two ideal in a regular local ring \(R\) of dimension \(d\) greater than or equal to three and let \(J\) be the intersection of all primary components of \(I\) of height two. If the projective dimension of \(R\) modulo \(J\) is two then the depth of \(R\) modulo \(I\) is greater than or equal to \(d\) minus three. This result is derived from a general and more elementary setting. A negative answer is given to the question of Huneke whether depth\(R\) modulo \(I\) is greater than or equal to depth\(R\) modulo \(J\) minus one if depth\(R\) modulo \(J\) is greater than or equal to two.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 13D05
zbMATH DE Number: 858615
zbMATH Keywords: ideal
zbMATH Keywords: regular local ring
zbMATH Keywords: projective dimension
reviewed by: Kwangil Koh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 858615