In their paper [Acta Math. Acad. Sci. Hung. 39, 11-15 (1982; Zbl 0441.16006)] \textit{G. A. P. Heyman}, \textit{T. L. Jenkins} and \textit{H. J. Le Roux} investigated the classes \(\alpha_ 1,\alpha_ 2,\alpha_ 3\) resp. of rings R such that every non-zero subring, left ideal, ideal resp. of R strictly contains a power of R. It is shown there that \(\beta\) \(\subseteq {\mathfrak L}\alpha_ 1\subsetneqq {\mathfrak L}\alpha_ 2\subseteq {\mathfrak L}\alpha_ 3\subseteq \beta_{\phi}\) \(\beta =lower\) Baer radical, \({\mathfrak L}\alpha_ i=lower\) radical generated by \(\alpha_ i\) and \(\beta_{\phi}=antisimple\) radical. In this paper the author shows that \(\alpha_ 1=the\) class of nilpotent rings, so \({\mathfrak L}\alpha_ 1=\beta\). One further result is that \({\mathfrak L}\alpha_ 2\neq {\mathfrak L}\alpha_ 3\) which contradicts a theorem in the above-cited paper. It is known that \({\mathfrak L}\alpha_ 3\subsetneqq \beta_{\phi}\) by an example of G. Tzintzis. The author also proves that \({\mathfrak L}\alpha_ 3\) is an N-radical.