On non Artinian cofinite generalized local cohomology modules
type: Item
instance of: scholarly article
title: On non Artinian cofinite generalized local cohomology modules
zbMATH Open document ID: 1496.13028
author: Farzaneh Vahdanipour
published in: Advanced Studies: Euro-Tbilisi Mathematical Journal
publication date: 2022-10-10T00:00:00Z
full work available at URL: 19322008223.full
review text: Let \(R\) be a commutative Noetherian ring and \(I\subseteq J\) be ideals of \(R\). Let \(M\) and \(N\) be finitely generated \(R\)-modules such that projective dimension of \(M\) is finite. Let \(q_I(M, N) = \sup\{i\in\mathbb{N}_0 : H^i_ I(M, N)\) is not Artinian I-cofinite\(\}\), where \(H^i_I(M,N)\) is the generalized local cohomology module. In the paper under review, the author proves that \(q_J(M, N)\le q_I(M, N)+ \mathrm{cd}_J(M, N/IN)\), where \(\mathrm{cd}_J(M,N/IN)\) is the cohomological dimension of \(m\) and \(N/IN\) with respect to ideal \(J\).
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14B15
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 7599156
zbMATH Keywords: cofinite module
zbMATH Keywords: cohomological dimension
zbMATH Keywords: generalized local cohomology module
zbMATH Keywords: Noetherian ring
MaRDI profile type: Publication
OpenAlex ID: W4301401610
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DOI: 10.32513/ASETMJ/19322008223
description: scientific article; zbMATH DE number 7599156