On the category of weakly Laskerian cofinite modules
type: Item
instance of: scholarly article
zbMATH Open document ID: 1306.13010
author: Kamal Bahmanpour
publication date: 2014-10-17T00:00:00Z
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 6357908
zbMATH Keywords: cofinite modules
zbMATH Keywords: local cohomology
zbMATH Keywords: weakly Laskerian modules
MaRDI profile type: Publication
full work available at URL: math.scand.a-18002
OpenAlex ID: W2179246247
DOI: 10.7146/MATH.SCAND.A-18002
title: On the category of weakly Laskerian cofinite modules
published in: Mathematica Scandinavica
review text: Let \(R\) be a Noetherian commutative ring with identity and \(I\) an ideal of \(R\). Recall that an \(R\)-module \(M\) is said to be \(I\)-cofinite if \(\text{Supp}_RM\subseteq V(I)\) and \(\text{Ext}_R^i(R/I,M)\) is finitely generated for all \(i\geq 0\). Also, \(M\) is said to be weakly Laskerian if any quotient module of \(M\) has finitely many associated prime ideals.NEWLINENEWLINEThe main achievement of this paper is to show that the category of \(I\)-cofinite weakly Laskerian \(R\)-modules forms an abelian subcategory of the category of all \(R\)-modules. Also, the author provides a nice characterization for weakly Laskerian modules. He proves that an \(R\)-module \(M\) is weakly Laskerian if and only if it possesses a submodule \(N\) such that \(\text{Supp}_RM/N\) is finite.
reviewed by: Kamran Divaani-Aazar
description: scientific article; zbMATH DE number 6357908