Normalizing extensions of semiprime rings.
type: Item
instance of: scholarly article
title: Normalizing extensions of semiprime rings.
zbMATH Open document ID: 1072.16022
author: Miguel Ferrero
author: Rogério Ricardo Steffenon
published in: Beiträge zur Algebra und Geometrie
publication date: 2004-09-01T00:00:00Z
full work available at URL: https://eudml.org/doc/228660
full work available at URL: 11.html
review text: The authors study normalizing extensions of semiprime rings. After studying various types of ring extensions in Section 1, in Section 2, for a normalizing extension \(S\) for a ring \(R\), they construct canonical torsion-free \(S^*\) and derive a one-to-one correspondence between the set of closed ideals of \(S\) and the set of closed ideals of \(S^*\). In Section 4, they study intermediate extensions and prove that the above results can be extended in this context also. Finally, in Section 5, they study strongly prime and non-singular prime ideals of the intermediate extensions and extend and improve most of the results of Ferrero.
Mathematics Subject Classification ID: 16S20
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 2096235
zbMATH Keywords: semiprime rings
zbMATH Keywords: nonsingular prime ideals
zbMATH Keywords: normalizing extensions
zbMATH Keywords: symmetric rings of quotients
zbMATH Keywords: centralizing extensions
zbMATH Keywords: closed ideals
zbMATH Keywords: strongly prime ideals
zbMATH Keywords: intermediate extensions
reviewed by: Veereshwar A. Hiremath
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2096235