Commutative rings for which every continuous module is quasi-injective
type: Item
instance of: scholarly article
title: Commutative rings for which every continuous module is quasi-injective
zbMATH Open document ID: 0631.13012
DOI: 10.1007/BF01196504
author: S. Tariq Rizvi
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: A module is called continuous if (i) every submodule is essential in a summand and \((ii)\quad every\) submodule, isomorphic to a summand, is itself a summand. It is well known that every quasi-injective module is continuous. The purpose of this paper is to study commutative rings for which every continuous module is quasi-injective. It is shown that large classes of commutative rings, such as noetherian rings, and semiprimary rings with Jacobson radical square zero, have this property. We provide necessary and sufficient conditions, for some classes of commutative rings such as finitary rings, perfect rings, and chain rings to have this property. A necessary and sufficient condition for an arbitrary commutative ring, for which every uniform continuous R-module is quasi- injective, is also given.
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13E99
zbMATH DE Number: 4025563
zbMATH Keywords: quasi-injective continuous module
MaRDI profile type: Publication
Wikidata QID: Q114234026
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full work available at URL: https://doi.org/10.1007/bf01196504
OpenAlex ID: W2085812461
description: scientific article; zbMATH DE number 4025563