Torsion theories and primary decomposition of modules
type: Item
instance of: scholarly article
title: Torsion theories and primary decomposition of modules
zbMATH Open document ID: 0596.16024
author: Binlong Zhang
published in: Chinese Annals of Mathematics. Series B
publication date: 1985-01-01T00:00:00Z
review text: The author studies rings \(R\) which have primary decompositions in the sense that every semiartinian left \(R\)-module is a direct sum of its primary submodules. If \(R\) is left semiartinian and every left \(R\)-module has a maximal submodule, then \(R\) is shown to have primary decomposition if and only if \(\Ext(S_1,S_2)=0\) for every pair of non-isomorphic simple modules, \(S_1\), \(S_2\). In this case it is also proved that all the torsion theories of \(R\)-mod are generated by simple modules.
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 3959702
zbMATH Keywords: primary decompositions
zbMATH Keywords: semiartinian left R-module
zbMATH Keywords: direct sum
zbMATH Keywords: primary submodules
zbMATH Keywords: maximal submodule
zbMATH Keywords: simple modules
zbMATH Keywords: torsion theories
reviewed by: José L. Gómez-Pardo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3959702