Quasi-injective modules with acc or dcc on essential submodules
type: Item
instance of: scholarly article
title: Quasi-injective modules with acc or dcc on essential submodules
zbMATH Open document ID: 0658.16018
DOI: 10.1007/BF01277059
author: Nguyen Viet Dung
author: Dinh Van Huynh
author: Robert Wisbauer
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: It is shown that finitely generated modules with the properties given in the title are noetherian resp. artinian. Another result in the paper is that the endomorphism ring of a quasi-injective, quasi-projective module with acc on essential submodules is a ring direct sum of a left artinian ring and a von Neumann regular, left self-injective ring. Also, a new characterization of QF-rings is given: A left self-injective ring with acc on essential left or right ideals is a QF-ring. Recall that [in \textit{E. Armendariz}, Commun. Algebra 8, 299-308 (1980; Zbl 0444.16015)], QF- rings are characterized as left self-injective rings with dcc on essential left or right ideals.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 4075320
zbMATH Keywords: finitely generated modules
zbMATH Keywords: endomorphism ring
zbMATH Keywords: quasi-projective module with acc on essential submodules
zbMATH Keywords: direct sum
zbMATH Keywords: left artinian ring
zbMATH Keywords: von Neumann regular, left self-injective ring
zbMATH Keywords: QF-rings
Wikidata QID: Q114233972
MaRDI profile type: Publication
cites work: Q4056148
cites work: Rings with dcc on essential left ideals
cites work: Q4040327
description: scientific article; zbMATH DE number 4075320