An example of a right \(q\)-ring
type: Item
instance of: scholarly article
title: An example of a right \(q\)-ring
zbMATH Open document ID: 1028.16001
DOI: 10.1007/BF02784536
published in: Israel Journal of Mathematics
publication date: 2003-11-03T00:00:00Z
review text: After being introduced by \textit{S. K. Jain, S. H. Mohamed} and \textit{S. Singh} [in Pac. J. Math. 31, 73-79 (1969; Zbl 0213.04401)], right \(q\)-rings motivated further work by several other authors. In particular, \textit{G. Ivanov} [Bull. Aust. Math. Soc. 6, 45-52 (1972; Zbl 0221.16012)] conjectured a certain characterization which was later shown not to be complete by \textit{K. A. Byrd} [in Pac. J. Math. 82, 23-41 (1979; Zbl 0416.16006)] where a complete characterization of such rings is proposed. Building on further work by \textit{S. K. Jain, S. R. López-Permouth} and \textit{S. R. Syed} [Glasg. Math. J. 41, No. 2, 167-181 (1999; Zbl 0943.16003)], this paper shows that Byrd's characterization is not complete either. The error in the proof (which apparently goes back to an error made by Ivanov (loc. cit.)) is corrected in the paper under review and the characterizations of Ivanov and Byrd are sharpened and completed.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16L30
zbMATH DE Number: 1786384
zbMATH Keywords: quasi-injective right modules
zbMATH Keywords: right \(q\)-rings
zbMATH Keywords: quasi-injective right ideals
author: K. I. Beidar
author: Y. Fong
author: Wen-Fong Ke
author: S. K. Jain
reviewed by: Sergio R. López-Permouth
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02784536
OpenAlex ID: W2316521649
description: scientific article; zbMATH DE number 1786384