Bounded regularity
type: Item
instance of: scholarly article
title: Bounded regularity
zbMATH Open document ID: 1304.13024
author: Claus Diem
published in: Journal of Algebra
publication date: 2014-12-05T00:00:00Z
review text: If \(S\) is a polynomial ring and \(M\) a finitely generated graded \(S\)-module, the author introduces the notion of a sequence \((f_1,\dots,f_r)\) of homogeneous polynomials which is regular up to a certain degree. For general modules \(M\), he then provides two characterisations of sequences regular up to a degree \(D\): one in terms of the Hilbert series of \(M/(f_1,\dots,f_r)M\) and one in terms of first syzygies. For the special case \(M=S\), two further characterisations are given: one via Betti numbers and one via the Koszul complex of the sequence and the minimal free resolution of the ideal generated by the sequence. Some applications of the results, in particular to the analysis of Faugeère's F5 algorithm for Gröbner bases computations, are given.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 6377609
zbMATH Keywords: polynomial ring
zbMATH Keywords: regularity
zbMATH Keywords: Fröberg's conjecture
zbMATH Keywords: Hilbert series
zbMATH Keywords: Betti numbers
zbMATH Keywords: Koszul complex
zbMATH Keywords: syzygies
describes a project that uses: F5C
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2014.09.029
OpenAlex ID: W4205593132
cites work: Modifying Faugère's F5 algorithm to ensure termination
cites work: Q4317713
cites work: The Geometry of Syzygies
cites work: F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
cites work: Q4660688
cites work: An inequality for Hilbert series of graded algebras.
cites work: Q3739243
cites work: Generic sequences of polynomials
cites work: Syzygies of semi-regular sequences
cites work: Errata for ``Syzygies of semi-regular sequences''
cites work: Hilbert functions of graded algebras
DOI: 10.1016/J.JALGEBRA.2014.09.029
description: scientific article; zbMATH DE number 6377609