On the category of confinite modules for principal ideals
type: Item
instance of: scholarly article
title: On the category of confinite modules for principal ideals
zbMATH Open document ID: 1247.14003
author: Ken-Ichiroh Kawasaki
published in: Nihonkai Mathematical Journal
publication date: 2012-06-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.nihmj/1339696712
review text: Let \(R\) be a noetherian commutative ring and \(I\) be an ideal of \(R\). Let \({\mathcal M}(R,I)_{\mathrm{cof}}\) be the collection of all \(R\)-modules \(X\) satisfying the two conditions: i) \(\mathrm{Supp}_R(X)\subseteq V(I)\) and ii) \(\mathrm{Ext}_R^j(R/I,X)\) is of finite type, for all \(j\). In this paper, it is shown that if \(I\) is generated by an element up to radical, then \({\mathcal M}(R,I)_{\mathrm{cof}}\) is an abelian full subcategory of the category of all \(R\)-modules. A counterexample for ideals generated by two elements was given by \textit{R. Hartshorne} [Invent. Math. 9, 145--164 (1970; Zbl 0196.24301)].
Mathematics Subject Classification ID: 14B15
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 18G15
zbMATH DE Number: 6050970
zbMATH Keywords: local cohomology
zbMATH Keywords: cofinite module
zbMATH Keywords: abelian category
reviewed by: Blas Torrecillas
MaRDI profile type: Publication
cites work: A characterization of cofinite complexes over complete Gorenstein domains
cites work: Cofinite modules and local cohomology
cites work: Affine duality and cofiniteness
cites work: Cofiniteness and vanishing of local cohomology modules
cites work: Cofiniteness of Local Cohomology Modules for Principal Ideals
cites work: On a category of cofinite modules which is abelian
cites work: Q3882615
description: scientific article; zbMATH DE number 6050970