Ratliff-Rush closures of ideals with respect to a noetherian module (Q1765697)

Let \(R\) be a noetherian ring, \(E\) a finitely generated \(R\)-module and \(I\) an ideal of \(R\). Assume that \(IE\neq E\) and that \(I\) contains an \(E\)-regular element. In answer to a question of \textit{W. Heinzer, B. Johnston, D. Lantz} and \textit{K. Shah} [in: Methods in module theory. Conference Colorado Springs, 1991, Lect. Notes Pure Appl. Math. 140, 149--159 (1993; Zbl 0794.13003)], the author shows that all sufficiently large powers of \(I\) are Ratliff-Rush closed with respect to \(E\). Several characterizations are also given of when all powers of \(I\) are Ratliff-Rush closed with respect to \(E\).