Modules and representations of nonassociative compact topological rings
type: Item
instance of: scholarly article
title: Modules and representations of nonassociative compact topological rings
zbMATH Open document ID: 0623.17014
DOI: 10.1007/BF01157026
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The necessary definitions can be found in the monograph of \textit{K. A. Zhevlakov}, \textit{A. M. Slin'ko}, \textit{I. P. Shestakov}, and \textit{A. I. Shirshov}, Nearly associative rings (Moscow, Nauka, 1978; Zbl 0445.17001); English translation Academic Press (1982; Zbl 0487.17001), chapter 11. It is proved that under certain restrictions on a variety \({\mathcal M}\) of rings every topologically irreducible locally compact R-module, R being a compact ring from \({\mathcal M}\), is finite. Using this result the following characterization of the quasiregular radical J(R) of a compact ring R from \({\mathcal M}\) is given, where \({\mathcal M}\) is the variety of alternative or Jordan rings: J(R) coincides with the intersection of all locally compact irreducible representations of the ring R in the variety \({\mathcal M}\).
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 17C50
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 16W80
zbMATH DE Number: 4010734
zbMATH Keywords: irreducible topological right modules
zbMATH Keywords: compact alternative and Jordan rings
zbMATH Keywords: variety of rings
zbMATH Keywords: quasiregular radical
zbMATH Keywords: variety of alternative or Jordan rings
author: Arkadii Slinko
reviewed by: Mihail I. Ursul
MaRDI profile type: Publication
Wikidata QID: Q61586490
cites work: Q3748453
cites work: Q3890908
cites work: Q3947798
cites work: Q5680270
cites work: A GENERAL THEORY OF JORDAN RINGS
full work available at URL: https://doi.org/10.1007/bf01157026
OpenAlex ID: W2060690243
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description: scientific article; zbMATH DE number 4010734