Constructing arbitrary torsion elements for a local cohomology module
type: Item
instance of: scholarly article
title: Constructing arbitrary torsion elements for a local cohomology module
zbMATH Open document ID: 1271.13035
author: Julian Chan
published in: Journal of Algebra
publication date: 2013-05-13T00:00:00Z
review text: Let \(R\) be a Noetherian ring and \(I\) an ideal. If \(\dim R/I > 0\), then local cohomology module \(H_I^p(R)\) has many strange properties. For example, \textit{A. K. Singh} [Math. Res. Lett. 7, No. 2--3, 165--176 (2000; Zbl 0965.13013)] showed the following: Let \[ R = \mathbb{Z}[U, V, W, X, Y, Z]/(UX + VY + WZ) \] and \(I = (X, Y, Z)\). Then, for any prime integer \(p\), the abelian group \(\mathbb{Z}/p \mathbb{Z}\) embeds into \(H_I^3(R)\). Consequently, \(H_I^3(R)\) has infinitely many associated primes. In the present paper, the author enlarges Singh's result. He shows that we can find arbitrary finitely generated abelian group in \(H_I^3(R)\).
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 6162678
zbMATH Keywords: cohomology modules
zbMATH Keywords: associated primes
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2012.07.016
OpenAlex ID: W2031332833
cites work: Q4026073
cites work: Bass Numbers of Local Cohomology Modules
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cites work: Bockstein homomorphisms in local cohomology
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DOI: 10.1016/J.JALGEBRA.2012.07.016
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description: scientific article; zbMATH DE number 6162678