A Briançon–Skoda Theorem for Isolated Singularities

LetAbe a normal Cohen–Macaulay local ring which is a homomorphic image of a Gorenstein local ring. Supposing thatAis pseudo-rational in the punctured spectrum, and that there exists a proper birational morphismX → Spec Asuch thatXis pseudo-rational, we show how one can find an integerk > 0 such that Infor all idealsI Aand integersn ≥ 0.