Examples in noncommutative localization
type: Item
instance of: scholarly article
title: Examples in noncommutative localization
zbMATH Open document ID: 0592.16009
DOI: 10.1016/0021-8693(86)90057-8
author: John A. Beachy
author: William D. Blair
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let R be a Noetherian ring and Q its Goldie localization at a prime ideal P. Using ideas from [\textit{L. W. Small} and \textit{J. T. Stafford}, J. Algebra 70, 156-161 (1981; Zbl 0478.16012)], the authors construct (i) an example of a ring R, finitely generated as a module over its Noetherian centre, for which the localization Q at a maximal ideal is neither left nor right Noetherian and (ii) an example where Q is Noetherian on one side only.
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16Dxx
zbMATH DE Number: 3950749
zbMATH Keywords: Noetherian ring
zbMATH Keywords: Goldie localization
zbMATH Keywords: prime ideal
zbMATH Keywords: Noetherian centre
zbMATH Keywords: maximal ideal
reviewed by: Paul M. Cohn
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90057-8
OpenAlex ID: W2028514731
cites work: On noncommutative localization
cites work: Inversive localization in noetherian rings
cites work: Localization in non-commutative Noetherian rings
cites work: A note on noncommutative localization
cites work: Localisation and completions of Noetherian PI algebras
cites work: Q3849050
description: scientific article; zbMATH DE number 3950749