Noetherian symbolic blow-ups (Q1176647)

\textit{P. C. Roberts} [Proc. Am. Math.Soc. 94, 589-592 (1985; Zbl 0589.13008)] gave a counterexample to the question whether the symbolic Rees ring \(R^{(P)}:=\oplus_{n\geq 0}P^{(n)}\) is Noetherian, where \(P\) is a prime ideal of the regular local ring \(R\), and \(P^{(n)}=P^ nR_ P\cap R\). A practical criterion to determine when \(R^{(P)}\) is Noetherian is given in the present paper, generalising to all dimensions a result of \textit{C. Huneke} [Mich. Math. J. 34, 293-318 (1987; Zbl 0628.13012)]. --- This is applied to give many examples where \(R^{(P)}\) is Noetherian.