Core of ideals of Noetherian local rings

The core of an ideal is the intersection of all its reductions. In 2005, Polini and Ulrich explicitly described the core as a colon ideal of a power of a single reduction and a power of for a broader class of ideals, where is an ideal in a local Cohen-Macaulay ring. In this paper, we show that if is an ideal of analytic spread in a Noetherian local ring with infinite residue field, then with some mild conditions on , we have for any minimal reduction of and for .