Reduction numbers of ideals
type: Item
instance of: scholarly article
title: Reduction numbers of ideals
zbMATH Open document ID: 0964.13003
published in: Journal of Algebra
publication date: 2001-07-16T00:00:00Z
review text: Let \(R\) be a Noetherian commutative ring with identity. For any ideal \(I\) of \(R\) the author defines the big reduction number \(\text{br}(I)\) of \(I\), and in case \(R\) is local, the reduction number \(\text{r}(I)\) of \(I\). General bounds for \(\text{br}(I)\) and \(\text{r}(I)\) in Noetherian rings for arbitrary ideals \(I\) and multiplicity bounds for \(m\)-primary ideals \(I\) in a Noetherian local ring \((R,m)\) are given.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 1340595
zbMATH Keywords: Gröbner basis
zbMATH Keywords: Hilbert function
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: primary ideal
zbMATH Keywords: big reduction number
author: Wolmer V. Vasconcelos
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: jabr.1998.7803
OpenAlex ID: W2002096960
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DOI: 10.1006/JABR.1998.7803
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description: scientific article; zbMATH DE number 1340595