Maximal Buchsbaum modules over Gorenstein local rings
type: Item
instance of: scholarly article
title: Maximal Buchsbaum modules over Gorenstein local rings
zbMATH Open document ID: 1098.13028
author: Mutsumi Amasaki
published in: Journal of Algebra
publication date: 2005-06-23T00:00:00Z
review text: Let \((A, \mathfrak{m})\) be a local Gorenstein ring of dimension \(d>0\), \(k=A/\mathfrak{m}\) and \(r=\dim_k (\mathfrak{m}/\mathfrak{m}^2).\) Let \(B\) be the set of all \(A\)-bases obtained permuting a fixed one. A noetherian \(A\)-module \(M\) is called maximal if \(\dim(M)=d\). \(M\) is called quasi-Buchsbaum if \(\mathfrak{m}H^i_{\mathfrak{m}}(M)=0\) for all \(i<\dim (M)\). The structure of maximal Buchsbaum modules over local Gorenstein rings is studied. It is proved that a maximal quasi-Buchsbaum module \(M\) is Buchsbaum if and only if \[ \mathfrak{m}\text{Ext}^i_A(M, A/\langle x_{r-n+1}, \dots, x_r\rangle)=0 \text{ for all }i>0, 0\leq n<d \] and \((x_1, \dots, x_r)\in B\).
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13C14
zbMATH DE Number: 2182062
zbMATH Keywords: Buchsbaum module
zbMATH Keywords: free resolution
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2005.01.050
OpenAlex ID: W2022536817
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DOI: 10.1016/J.JALGEBRA.2005.01.050
description: scientific article; zbMATH DE number 2182062