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Matematicheskie Zametki, 1997, Volume 61, Issue 4, Pages 596–611
DOI: https://doi.org/10.4213/mzm1538 (Mi mzm1538) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Stable subsets of modules and the existence of a unit in associative rings

A. V. Khokhlov
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DOI: https://doi.org/10.4213/mzm1538
Abstract: We obtain criteria for the existence of a (left) unit in rings (arbitrary, Artinian, Noetherian, prime, and so on) that are based on the systematic study of properties of stable subsets of modules and their stabilizers that generalize the technique of idempotents. We study a class of quasiunitary rings that is a natural extension of classes of rings with unit and of von Neumann (weakly) regular rings, which inherits may properties of these classes. Some quasiunitary radicals of arbitrary rings are constructed, and the size of these radicals “measures the probability” of the existence of a unit.
Received: 09.12.1994
English version:
Mathematical Notes, 1997, Volume 61, Issue 4, Pages 495–509
DOI: https://doi.org/10.1007/BF02354994
Bibliographic databases:
UDC: 512
Language: Russian
Citation: A. V. Khokhlov, “Stable subsets of modules and the existence of a unit in associative rings”, Mat. Zametki, 61:4 (1997), 596–611; Math. Notes, 61:4 (1997), 495–509
Citation in format AMSBIB
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\paper Stable subsets of modules and the existence of a~unit in associative rings
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\yr 1997
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\issue 4
\pages 596--611
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\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 4
\pages 495--509
\crossref{https://doi.org/10.1007/BF02354994}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XR25700033}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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