A Briançon-Skoda theorem for isolated singularities (Q1270971)

This paper contains various generalizations of the Briançon-Skoda theorem for pseudo-rational rings, namely results of the form \(\overline{{I^{n+k}}} \subseteq J I^n\), where \(I\) is an ideal, \(n\) an arbitrary integer, \(k\) an invariant of the ring, and \(J\) either the whole ring or the coefficient ideal of \(I\) with respect to some minimal reduction of \(I\). Here, the coefficient ideals are in the sense of \textit{I. M. Aberbach} and \textit{C. Huneke} [Math. Ann. 297, No. 2, 343-369 (1993; Zbl 0788.13001)]. Computable upper bounds on \(k\) are also proved.