Monomorphisms and radicals of Noetherian rings (Q1076773)

It is still an open question, raised by \textit{G. Renault} [Commun. Algebra 7, 753-761 (1979; Zbl 0397.16003)], whether the nilpotent radical N is mapped into itself by any monomorphism f of a right noetherian ring R. The problem has a positive answer, due to \textit{A. V. Jategaonkar} [J. Algebra 21, 51-59 (1972; Zbl 0233.16003)], when R is right artinian. The author provides an affirmative answer for the case of a right noetherian ring R satisfying the ascending chain condition for left annihilators. Consequently, the nilpotent radical of the Ore extension R[x;f] is of the form N[x;f]. The proof is elementary and elegant.