An example of a right \(q\)-ring
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.
scientific article; zbMATH DE number 1786384
scientific article