A note on almost nilpotent rings
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.
scientific article; zbMATH DE number 3993779