On essential extensions of direct sums of injective modules
type: Item
instance of: scholarly article
title: On essential extensions of direct sums of injective modules
zbMATH Open document ID: 1020.16001
author: Wen-Fong Ke
author: K. I. Beidar
published in: Archiv der Mathematik
publication date: 2002-05-21T00:00:00Z
review text: A well-known theorem by Matlis and Papp says that a ring \(R\) is right Noetherian if and only if the direct sum of any collection of injective right \(R\)-modules is injective. In this paper the authors give a nice generalization of this theorem by proving that a ring \(R\) is right Noetherian if and only if any essential extension of the direct sum of any family of injective right \(R\)-modules is a direct sum of injective modules.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 1742826
zbMATH Keywords: essential extensions
zbMATH Keywords: direct sums of injective modules
zbMATH Keywords: right Noetherian rings
Wikidata QID: Q114232162
reviewed by: Dinh Van Huynh
MaRDI profile type: Publication
full work available at URL: s00013-002-8224-2
OpenAlex ID: W2003134541
DOI: 10.1007/S00013-002-8224-2
description: scientific article; zbMATH DE number 1742826