The topological Jacobson radical of rings. I.
type: Item
instance of: scholarly article
title: The topological Jacobson radical of rings. I.
zbMATH Open document ID: 1262.16049
author: V. V. Tenzina
author: S. T. Glavatskii
author: A. V. Mikhalev
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-01-10T00:00:00Z
review text: The authors give a new definition for a topological Jacobson radical of a topological ring \(R\) as the intersection of annihilators of all topologically irreducible left \(R\)-modules. They show that this definition coincides with the classical definition. Several properties of the topological Jacobson radical are further studied. They also show that any topological ring can be embedded as a closed ideal into a unital ring so that the topological Jacobson radicals of these two rings coincide. It is proved that the topological Jacobson radical of a direct product of topological rings coincides with the direct product of topological Jacobson radicals of the rings involved. Also some properties of topological Jacobson radicals connected with the ring of continuous functions are established.
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 54H13
Mathematics Subject Classification ID: 16N40
zbMATH DE Number: 6124254
zbMATH Keywords: topological rings
zbMATH Keywords: topological Jacobson radical
zbMATH Keywords: topologically irreducible modules
zbMATH Keywords: nilpotent ideals
zbMATH Keywords: everywhere dense subrings
zbMATH Keywords: topologically overnilpotent radicals
reviewed by: Mart Abel
MaRDI profile type: Publication
full work available at URL: s10958-012-0910-4
OpenAlex ID: W4206261710
cites work: Q5340984
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cites work: Topological Rings
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DOI: 10.1007/S10958-012-0910-4
description: scientific article; zbMATH DE number 6124254