A note on almost nilpotent rings
type: Item
instance of: scholarly article
title: A note on almost nilpotent rings
zbMATH Open document ID: 0614.16006
DOI: 10.1007/BF01951354
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: The author makes some observations on the classes \(\alpha\), \(\alpha_ r\), \(\alpha_{\ell}\), \(\alpha_ s\) of all rings R such that every nonzero ideal, left ideal, right ideal, subring of R, respectively, strictly contains a power of R. First, he presents briefly results and related questions, on the above classes, of the papers of \textit{G. A. P. Heyman}, \textit{T. L. Jenkins}, \textit{H. J. Le Roux} [Acta Math. Acad. Sci. Hung. 39, 11-15 (1982; Zbl 0441.16006)] and \textit{A. D. Sands} [Acta Math. Hung. 45, 41-43 (1985; Zbl 0571.16006)], and he answers again the quoted questions using arguments which differ a little from those used by Sands. Finally, he gives a new proof of the fact that the radical \(L\alpha\) is left and right strong.
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 16Dxx
zbMATH DE Number: 3993779
zbMATH Keywords: almost nilpotent rings
zbMATH Keywords: prime radical
zbMATH Keywords: left hereditary class
author: E. R. Puczyłowski
MaRDI profile type: Publication
cites work: Q5513080
cites work: Q3921360
cites work: ON QUESTIONS CONCERNING STRONG RADICALS OF ASSOCIATIVE RINGS
cites work: Radicals and Morita contexts
cites work: On almost nilpotent rings
description: scientific article; zbMATH DE number 3993779