Localization, completion and the AR property in Noetherian P.I. rings

Given a prime ideal P in a noetherian ring R we examine the following two properties: (1) P is Ore localizable. (2) The completion of R at P is Noetherian. For rings satisfying the 2nd layer condition a strong connection is discovered between (1) and (2) and consequently questions by Goldie and McConnell are answered. As a corollary we also obtain a new characterization for non-maximal primitive ideal P in R to satisfy (1), where R is the enveloping algebra of complex solvable finite dimensional Lie algebra.