Socle finiteness of the local cohomology
type: Item
instance of: scholarly article
title: Socle finiteness of the local cohomology
zbMATH Open document ID: 1209.13020
DOI: 10.1216/RMJ-2011-41-1-299
author: Jan Trlifaj
author: M. Tamer Koşan
published in: Rocky Mountain Journal of Mathematics
publication date: 2011-03-01T00:00:00Z
review text: Let \(R\) be a commutative local noetherian ring. Finiteness properties of local cohomology modules over \(R\) are among the basic topics of local cohomology theory. One of the main question is as follows ``Let \(I\) be an ideal of \(R\). Is the socle of \(H^n_I(R)\) finitely generated?'' A positive answer to this question for all regular local ring was conjectured by Huneke. In the paper under review the authors proved the following result: Theorem. Let \(R\) be a regular local ring, and let \(I\) be an ideal with level prime avoidance. Then the socle of \(H^n_I(R)\) is finitely generated.
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14B15
zbMATH DE Number: 5858892
zbMATH Keywords: local cohomology
zbMATH Keywords: regular local ring
zbMATH Keywords: socle
Wikidata QID: Q57571128
MaRDI profile type: Publication
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full work available at URL: rmj-2011-41-1-299
OpenAlex ID: W2038901561
description: scientific article; zbMATH DE number 5858892