Recurrent behavior in rings
type: Item
instance of: scholarly article
title: Recurrent behavior in rings
zbMATH Open document ID: 0633.16004
DOI: 10.1016/0021-8693(87)90126-8
author: Daniel R. Farkas
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: This paper discusses the parallel development of certain group theoretic techniques used in the study of group rings and in ergodic theory. Section 1 compares the \(\Delta\)-methods to syndetic and thick sets. Section 2 considers the recurrence capacity of a group action. Section 3 is concerned with the relationship between ergodic theory and the group ring results of \textit{G. Bergman} [Trans. Am. Math. Soc. 157, 459-470 (1971; Zbl 0197.17102)] and \textit{J. E. Roseblade} [Proc. Lond. Math. Soc., III. Ser. 36, 385-447 (1978; Zbl 0391.16008)]. Finally, Section 4 compares almost nilpotent group actions to distal actions. Referees comments. It would appear from this paper that group ring results are now sufficiently powerful to yield algebraic analogues of some basic results in ergodic theory and dynamical systems. In fact these analogs are frequently stronger since they hold in noncommutative situations. Thus there might be some fruitful applications to this direction. On the other hand, it is not clear from this paper that ergodic theory has much to offer the study of group rings other than its colorful notation.
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 4029768
zbMATH Keywords: group rings
zbMATH Keywords: recurrence capacity
zbMATH Keywords: group action
zbMATH Keywords: distal actions
zbMATH Keywords: ergodic theory
zbMATH Keywords: dynamical systems
reviewed by: D. S. Passman
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90126-8
OpenAlex ID: W1972266382
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description: scientific article; zbMATH DE number 4029768