On \((\aleph,U)\)-coherence of modules and rings.
type: Item
instance of: scholarly article
title: On \((\aleph,U)\)-coherence of modules and rings.
zbMATH Open document ID: 1068.16002
publication date: 2004-11-26T00:00:00Z
review text: Let \(U\) be a flat right \(R\)-module and let \(\aleph\) be an infinite cardinal number. A left \(R\)-module \(M\) is called \((\aleph,U)\)-coherent if every finitely presented \(M\)-projective in \(\sigma[M]\) is \((\aleph,U)\)-finitely generated in \(\sigma[M]\). Using the methods of \textit{P. Loustaunau} [Commun. Algebra 17, No. 1, 197-215 (1989; Zbl 0664.16019)], \textit{L. Oyonarte} and \textit{B. Torrecillas} [ibid. 24, No. 4, 1389-1407 (1996; Zbl 0845.16003)], etc., products of certain right \(R\)-modules are \(R\)-flat modules. The concept of an \((\aleph,U)\)-coherent dimension is defined and studied.
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16P70
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 2119275
zbMATH Keywords: flat modules
zbMATH Keywords: \((\aleph,U)\)-coherence
zbMATH Keywords: \((\aleph, U)\)-coherent dimension
zbMATH Keywords: finitely presented modules
author: Zhongkui Liu
author: Javed Ahsan
reviewed by: Mark L. Teply
MaRDI profile type: Publication
full work available at URL: s10114-003-0294-y
OpenAlex ID: W2006522391
cites work: Large subdirect products of projective modules
cites work: Large subdirect products of flat modules
cites work: On relative coherence and applications∗
cites work: Coherence relative to an hereditary torsion theory
cites work: Left \(\aleph\)-coherent dimension of rings
cites work: Q4002547
cites work: Large subdirect products of graded modules
cites work: Subdirect products of injectives
cites work: Uniform dimension and subdirect products
cites work: Q3764300
cites work: N-Products of injective objects in grothendieck categories
cites work: On right duo p.p. rings
DOI: 10.1007/S10114-003-0294-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2119275