Localization in prime Noetherian P.I. rings
type: Item
instance of: scholarly article
title: Localization in prime Noetherian P.I. rings
zbMATH Open document ID: 0611.16013
DOI: 10.1007/BF01229800
author: A. Braun
author: Lance W. Small
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173788
review text: 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.]
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16Dxx
zbMATH DE Number: 3987498
zbMATH Keywords: affine prime noetherian PI ring
zbMATH Keywords: left localizable
zbMATH Keywords: right localizable
zbMATH Keywords: trace ring
zbMATH Keywords: localization
zbMATH Keywords: symbolic powers of a prime ideal
reviewed by: T. H. Lenagan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3987498