Regularity of modules over a Koszul algebra
type: Item
instance of: scholarly article
title: Regularity of modules over a Koszul algebra
zbMATH Open document ID: 0770.13006
DOI: 10.1016/0021-8693(92)90149-G
author: David Eisenbud
author: Luchezar L. Avramov
published in: Journal of Algebra
publication date: 1993-03-28T00:00:00Z
review text: If \(R\) is a graded Noetherian \(k\)-algebra generated in degree 1, for \(k\) a field, the regularity \(\text{reg}_ RM\) of a module \(M\) is the infimum of the integers \(r\) such that for all \(i\geq 0\), \(\text{Tor}^ R_ i(M,k)_{i+s}=0\) for all \(s>r\). A Koszul algebra is a ring \(R\) as above such that \(\text{reg}_ Rk=0\). --- In this paper it is proved that if \(R\) is a Koszul algebra and \(Q=k[R_ 1]\) is the polynomial ring mapping onto \(R\), then the regularity of any module \(M\) over \(R\) is finite and \(\text{reg}_ RM\leq\text{reg}_ QM\). This is used to derive results on the existence on linear resolutions.
reviewed by: Timothy Porter
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 130475
zbMATH Keywords: graded Noetherian algebra
zbMATH Keywords: regularity of a module
zbMATH Keywords: Koszul algebra
zbMATH Keywords: linear resolutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 130475