On the arithmetical rank of monomial ideals
type: Item
instance of: scholarly article
title: On the arithmetical rank of monomial ideals
zbMATH Open document ID: 0639.13015
DOI: 10.1016/0021-8693(88)90133-0
author: Gennady Lyubeznik
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: If I is an ideal of a commutative ring A, then the arithmetical rank of I, \(ara_ A I\), is the minimum number of elements of A generating I up to radical. The author proves the following theorem: Let A be the polynomial ring \(k [X_ 0,...,X_ n]\) in \(n + 1\) indeterminates, localized at \((X_ 0,...,X_ n)\), with k an infinite field, and let I be an ideal generated by monomials in the \(X_ i\) such that all its minimal prime ideals are of height \(\leq t\). Then \(ara_ A I \leq n + 1 - [n / t].\)
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 4042050
zbMATH Keywords: monomial ideals
zbMATH Keywords: symbolic Rees algebras
zbMATH Keywords: number of generators of ideal
zbMATH Keywords: arithmetical rank
zbMATH Keywords: minimal prime ideals
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90133-0
OpenAlex ID: W2074447092
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description: scientific article; zbMATH DE number 4042050