Zero-divisors in completions of non-commutative rings
type: Item
instance of: scholarly article
title: Zero-divisors in completions of non-commutative rings
zbMATH Open document ID: 0784.16025
DOI: 10.1007/BF02808076
author: David A. Jordan
published in: Israel Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: An example is constructed of a Noetherian ring \(R\) with the following properties: there is a maximal ideal \(M\) of \(R\) such that \(R/M\) is Artinian and the intersection of the powers of \(M\) is 0; and there is a regular normal element \(x\) of \(R\) such that \(x\) becomes a zero divisor in the completion of \(R\) at \(M\). This contrasts with the fact that if \(R\) is commutative then \(x\) remains regular in the completion.
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 219422
zbMATH Keywords: Noetherian ring
zbMATH Keywords: maximal ideal
zbMATH Keywords: regular normal element
zbMATH Keywords: zero divisor
zbMATH Keywords: completion
reviewed by: A. W. Chatters
MaRDI profile type: Publication
cites work: Completions of Noetherian P.I. rings
cites work: Note on Non-Commutative Semi-Local Rings
cites work: Normal Elements and Completions of Non-Commutative Noetherian Rings
cites work: Normalizing Sequences and Completions of Non-Commutative Noetherian Rings
cites work: Integrality of I-adic completions
cites work: Q3739243
cites work: I-adic completions of non-commutative rings
cites work: Q3786586
cites work: Q5542855
cites work: Q4049223
cites work: Local Rings and Normalizing Sets of Elements
full work available at URL: https://doi.org/10.1007/bf02808076
OpenAlex ID: W1999670637
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description: scientific article; zbMATH DE number 219422