New characterizations of Artinian modules and hereditary rings
type: Item
instance of: scholarly article
title: New characterizations of Artinian modules and hereditary rings
zbMATH Open document ID: 0744.16012
author: Azmi Hanna
published in: Beiträge zur Algebra und Geometrie
publication date: 1992-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/138472
review text: Let \(R\) be an associative ring with 1. The author proves that a left \(R\)- module \(M\) is Artinian iff every non-empty set of finitely cogenerated factor modules of \(M\) has a maximal element, and that \(R\) is left hereditary iff in every projective left \(R\)-module \(M\) the intersection \(U\cap V\) of two direct summands \(U\) and \(V\) of \(M\) is also a direct summand of \(M\).
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 21340
zbMATH Keywords: Artinian modules
zbMATH Keywords: hereditary rings
zbMATH Keywords: finitely cogenerated factor modules
zbMATH Keywords: projective left \(R\)-module
zbMATH Keywords: direct summands
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 21340