Integral closures of ideals of the principal class (Q1101512)

Let \({\mathfrak q}\) be an ideal of the principal class in a locally quasi- unmixed Noetherian ring. Then \({\mathfrak q}^ n\cap ({\mathfrak q}^{n+1})^*={\mathfrak q}^ n{\mathfrak q}^*\), for all \(n\geq 0\), where ( )\({}^*\) denotes integral closure. This extends a result of \textit{C. Huneke} [Mich. Math. J. 34, 293-318 (1987; Zbl 0628.13012)].