Stable torsion radicals over Noetherian rings (Q798746)

This note is a discussion, in torsion-theoretic language, of two properties of a left Noetherian ring R, namely smoothness, as defined by \textit{K. A. Brown} [J. Algebra 69, 247-260 (1981; Zbl 0471.16012)] and condition \(\left( \begin{matrix} *\\ *\end{matrix} \right)\), [\textit{A. V. Jategaonkar}, Commun. Algebra 10, 19-69 (1982; Zbl 0476.16014)]. The author observes, among other things, that R is left smooth if and only if it satisfies \(\left( \begin{matrix} *\\ *\end{matrix} \right)\) on the left and the bimodules I/J, where I and J are ideals of R, satisfy a certain ''Krull symmetry'' condition.