The lcm-lattice in monomial resolutions
type: Item
instance of: scholarly article
title: The lcm-lattice in monomial resolutions
zbMATH Open document ID: 0970.13004
author: Irena Peeva
author: Volkmar Welker
author: Vesselin Gasharov
published in: Mathematical Research Letters
publication date: 2000-08-13T00:00:00Z
review text: For each monomial ideal \(I\) of a polynomial ring \(S\) (in \(n\) variables over a field \(k)\) which is generated by a sequence of monomials a lattice \({\mathcal L}_I\) is constructed which consists of least common multiples of subsequences of this sequence. It is proved that the lattice \({\mathcal L}_I\) determines the Betti numbers and the minimal free resolution of \(S/I\) and also the algebra structure on \(\text{Tor}^S (S/I,k)\) if additional data in \({\mathcal L}_I\), whose pairs of minimal monomial generators are relatively prime, are known.
reviewed by: Stanisław Balcerzyk
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13D07
zbMATH DE Number: 1489535
zbMATH Keywords: monomial ideal
zbMATH Keywords: Betti numbers
zbMATH Keywords: minimal free resolution
MaRDI profile type: Publication
DOI: 10.4310/MRL.1999.V6.N5.A5
description: scientific article; zbMATH DE number 1489535