On generating sets of minimal length for polynomial ideals
type: Item
instance of: scholarly article
title: On generating sets of minimal length for polynomial ideals
zbMATH Open document ID: 0614.13009
author: H. Bresinsky
author: Bodo Renschuch
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138369
review text: Let \(A=K[X_ 1,...,X_ n]\) be the polynomial ring in n indeterminates over a field K. For an ideal I of A, let \(\mu(I)\) denote the smallest integer such that I can be generated by \(\mu(I)\) elements. The authors find a class of counter-examples where a set of generators of I corresponding to a homogeneous set of generators of the associated homogeneous ideal (or even the so called Gröbner basis) does not contain a generating set of I of cardinality \(\mu(I).\) The authors also discuss the problem of finding an algorithm to determine \(\mu(P)\) for a prime ideal P of A.
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 3993735
zbMATH Keywords: number of generators of ideals
zbMATH Keywords: polynomial ring
zbMATH Keywords: associated homogeneous ideal
zbMATH Keywords: Gröbner basis
zbMATH Keywords: algorithm
reviewed by: Balwant Singh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3993735