A natural map in local cohomology
type: Item
instance of: scholarly article
title: A natural map in local cohomology
zbMATH Open document ID: 1225.13021
author: Moharram Aghapournahr
author: Leif Melkersson
published in: Arkiv för Matematik
publication date: 2010-10-26T00:00:00Z
review text: In the paper under review the authors study the finiteness properties of the kernel and cokernel of the natural map from some Ext-modules to the \(\mathfrak a\)-annihalator of the local cohomology module and then give some results on associated primes and Artinian property of some local cohomology modules. Let \(R\) be a Noetherian ring, \(\mathfrak a\) an ideal of \(R\), \(M\) an \(R\)-module and \(n\) be a non-negative integer. Let \(f:\text{Ext}^n_R(R/\mathfrak a,M)\to\Hom_R(R/\mathfrak a,H^n_{\mathfrak a}(M))\) be the natural map. The authors, under some conditions on the previous local cohomology modules, study some properties of \(\text{Ker\,}f\) and \(\text{Coker\,}f\). Then, in the graded setting, they get some results on asymptotic behavior of \(\text{Ker\,}f\) and \(\text{Coker\,}f\).
reviewed by: Naser Zamani
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13D07
zbMATH DE Number: 5805960
zbMATH Keywords: Serre subcategory
zbMATH Keywords: local cohomology
zbMATH Keywords: weakly Laskerian modules
MaRDI profile type: Publication
full work available at URL: s11512-009-0115-3
OpenAlex ID: W2095501682
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DOI: 10.1007/S11512-009-0115-3
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description: scientific article; zbMATH DE number 5805960