Localization in prime Noetherian P.I. rings
Let R be an affine prime noetherian PI ring that is a finite module over its centre and \(P\in spec(R)\). The authors show that P is left localizable if and only if P is right localizable and it follows, by a result of Mueller, that in this case the localization is central. The main tool used is the trace ring and to utilize this it is shown that the trace ring of a localization is the localization of the trace ring. As a second part of the paper the authors consider whether, in a prime noetherian PI ring, knowing that the intersection of the symbolic powers of a prime ideal is zero is sufficient to show that the prime is localizable. This is known not to be true in general but they show that it is true if the ring is a trace ring. [Reviewer's note: In a forthcoming paper, the first author and R. B. Warfield have shown that the left-right symmetry of localization holds for any prime noetherian PI ring.]
scientific article; zbMATH DE number 3987498
scientific article