Weakly stable ideals
type: Item
instance of: scholarly article
title: Weakly stable ideals
zbMATH Open document ID: 0901.13003
author: Jürgen Herzog
author: Takayuki Hibi
author: Annetta G. Aramova
published in: Osaka Journal of Mathematics
publication date: 1998-04-19T00:00:00Z
review text: Stable ideals are some monomial ideals introduced by \textit{S. Eliahou} and \textit{M. Kervaire} [J. Algebra 129, No. 1, 1-25 (1990; Zbl 0701.13006)], who gave explicitly their minimal free resolutions. These resolutions are linear if we consider only stable ideals generated by monomials of the same degree. The present paper introduces a class of squarefree monomial ideals, the so called weakly stable ideals, for which there exist still nice formulas for graded Betti numbers. For weakly stable ideals \(I\) generated by monomials of the same degree the authors give explicitly the minimal free resolutions, which are still linear. These resolutions are subcomplexes of the minimal free resolutions of the stable closure of \(I\).
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 1132986
zbMATH Keywords: graded Betti numbers
zbMATH Keywords: linear resolutions
zbMATH Keywords: weakly stable ideals
zbMATH Keywords: Koszul homology
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1132986