Monomorphisms and radicals of Noetherian rings
type: Item
instance of: scholarly article
title: Monomorphisms and radicals of Noetherian rings
zbMATH Open document ID: 0594.16008
DOI: 10.1016/0021-8693(86)90046-3
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: It is still an open question, raised by \textit{G. Renault} [Commun. Algebra 7, 753-761 (1979; Zbl 0397.16003)], whether the nilpotent radical N is mapped into itself by any monomorphism f of a right noetherian ring R. The problem has a positive answer, due to \textit{A. V. Jategaonkar} [J. Algebra 21, 51-59 (1972; Zbl 0233.16003)], when R is right artinian. The author provides an affirmative answer for the case of a right noetherian ring R satisfying the ascending chain condition for left annihilators. Consequently, the nilpotent radical of the Ore extension R[x;f] is of the form N[x;f]. The proof is elementary and elegant.
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 3955139
zbMATH Keywords: nilpotent radical
zbMATH Keywords: monomorphism
zbMATH Keywords: right noetherian ring
zbMATH Keywords: ascending chain condition for left annihilators
zbMATH Keywords: Ore extension
author: Caron Dean
reviewed by: Günter Krause
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90046-3
OpenAlex ID: W1984856945
cites work: Skew polynomial rings over orders in Artinian rings
cites work: Anneaux de polynomes de ore sur des anneaux artiniens
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description: scientific article; zbMATH DE number 3955139