On minimax and generalized local cohomology modules
type: Item
instance of: scholarly article
title: On minimax and generalized local cohomology modules
zbMATH Open document ID: 1195.13021
author: Hero Saremi
published in: Acta Mathematica Vietnamica
publication date: 2010-09-07T00:00:00Z
full work available at URL: Toc ACTA 2 34.htm
review text: Let \(\mathfrak a\) be an ideal of a commutative noetherian ring \(R\) and \(M,N\) two finitely generated \(R\)-modules. The paper concerns the finiteness properties of the generalized local cohomology modules \(H_{\mathfrak a}^i(M,N):={\varinjlim}_n\mathrm{Ext}^i_R(M/{\mathfrak{a}}^nM,N)\). Recall that an \(R\)-module \(K\) is said to be minimax if it has a finitely generated submodule such that the quotient by it is Artinian. Let \(t\) be a non-negative integer. The author showed that if \(H_{\mathfrak a}^i(R,N)\) is minimax for all \(i<t\), then \(H_{\mathfrak a}^i(M,N)\) is minimax for all \(i<t\). Also, she proved that if \(H_{\mathfrak a}^i(M,N)\) is minimax for all \(i<t\), then for any minimax submodule \(L\) of \(H_{\mathfrak a}^t(M,N)\), the \(R\)-module \(\Hom_R(R/\mathfrak a,H_{\mathfrak a}^t(M,N)/L)\) is finitely generated.
reviewed by: Kamran Divaani-Aazar
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 5780183
zbMATH Keywords: associated prime ideals
zbMATH Keywords: cofinite modules
zbMATH Keywords: generalized local cohomology modules
zbMATH Keywords: minimax modules
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5780183