Stable torsion radicals over Noetherian rings
type: Item
instance of: scholarly article
title: Stable torsion radicals over Noetherian rings
zbMATH Open document ID: 0547.16008
DOI: 10.1016/0022-4049(84)90059-8
author: John A. Beachy
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: This note is a discussion, in torsion-theoretic language, of two properties of a left Noetherian ring R, namely smoothness, as defined by \textit{K. A. Brown} [J. Algebra 69, 247-260 (1981; Zbl 0471.16012)] and condition \(\left( \begin{matrix} *\\ *\end{matrix} \right)\), [\textit{A. V. Jategaonkar}, Commun. Algebra 10, 19-69 (1982; Zbl 0476.16014)]. The author observes, among other things, that R is left smooth if and only if it satisfies \(\left( \begin{matrix} *\\ *\end{matrix} \right)\) on the left and the bimodules I/J, where I and J are ideals of R, satisfy a certain ''Krull symmetry'' condition.
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 3871576
zbMATH Keywords: Krull dimension
zbMATH Keywords: left Noetherian ring
zbMATH Keywords: smoothness
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90059-8
OpenAlex ID: W2009564088
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description: scientific article; zbMATH DE number 3871576