Boundedness in locally compact rings
type: Item
instance of: scholarly article
title: Boundedness in locally compact rings
zbMATH Open document ID: 0804.16045
DOI: 10.1016/0166-8641(94)90062-0
published in: Topology and its Applications
publication date: 1995-01-12T00:00:00Z
review text: Let \(R\) be a topological ring and \(M\) a topological \((R,R)\)-bimodule. If on the product \(R\times M\) of the topological groups \(R(+)\) and \(M(+)\) the multiplication is defined by \((r,m)\cdot(r',m')= (r\cdot r',m\cdot r'+ r\cdot m')\), then \(R\times M\) becomes a topological ring. If \(R\) is a locally compact ring, the group \(R^*\) of characters of the group \(R(+)\) is a topological \((R,R)\)-bimodule in a natural way, therefore the ring \(R\times R^*\) can be considered. In the paper is studied the question when for every topological \((R,R)\)-bimodule \(M\) (and, in particular, for a locally compact ring \(R\) for the \((R,R)\)-bimodule \(M = R^*\)) the topological ring \(R\times M\) is left bounded, right bounded.
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 16D20
Mathematics Subject Classification ID: 22A30
zbMATH DE Number: 500697
zbMATH Keywords: topological rings
zbMATH Keywords: topological \((R,R)\)-bimodules
zbMATH Keywords: topological groups
zbMATH Keywords: locally compact rings
zbMATH Keywords: left bounded rings
zbMATH Keywords: right bounded rings
author: Mihail I. Ursul
reviewed by: Vladimir Arnautov
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90062-0
OpenAlex ID: W2075394807
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description: scientific article; zbMATH DE number 500697