Algebraic rings with compact topology
type: Item
instance of: scholarly article
title: Algebraic rings with compact topology
zbMATH Open document ID: 0602.17015
DOI: 10.1007/BF01987300
published in: Algebra and Logic
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187339
review text: Let \(\Phi\) be a commutative associative ring with 1 (and \(1/2\) in the case of Jordan \(\Phi\)-algebras), which is also a Hausdorff topological ring. The author's main results are as follows: (1) Let \(\Gamma\) be a countable or compact ideal in \(\Phi\). If an alternative or Jordan compact topological \(\Phi\)-algebra is algebraic over \(\Gamma\), then it is algebraic over \(\Gamma\) of bounded index; and so such algebra is locally finite over \(\Gamma\). (2) In an alternative or Jordan compact ring, the McCrimmon radical coincides with the nil radical. Furthermore, every compact alternative or special Jordan nil-ring is solvable. Examples are given which show this last assertion is the best possible. Special cases of both these results were obtained earlier by \textit{M. I. Ursul} [Mat. Zametki 36, No. 6, 839--845 (1984; Zbl 0575.16022)].
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 17C99
Mathematics Subject Classification ID: 22A99
zbMATH DE Number: 3971004
zbMATH Keywords: affirmative solution of Kurosh problem
zbMATH Keywords: locally finite
zbMATH Keywords: McCrimmon radical
zbMATH Keywords: nil radical
zbMATH Keywords: nil-ring
Wikidata QID: Q61586476
author: Arkadii Slinko
MaRDI profile type: Publication
cites work: Q5509036
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cites work: On local finiteness in the sense of Shirshov
cites work: Compact nilrings
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OpenAlex ID: W1998945950
description: scientific article; zbMATH DE number 3971004