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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2015, Volume 15, Issue 3, Pages 30–50 (Mi vngu374)  
This article is cited in 2 scientific papers (total in 2 papers)

On potential counterexamples to the problem of zero divisors

V. G. Bardakovab, M. S. Petukhovaa

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (338 kB) Citations (2)
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Abstract: E. Rips constructed a serie of groups such that their group rings have zero divisors. These groups are possible counterexamples to Kaplansky problem on zero divisors. The main problem is to find inside this serie a group without torsion. In this paper are studied simplest groups of this serie. It is given their full classification, described their structure and proven that all of them have 2-torsion.
Keywords: problem on zero divisors, group without torsion, group ring.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00014
15-01-00745
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
Received: 19.03.2015
English version:
Journal of Mathematical Sciences, 2017, Volume 221, Issue 6, Pages 778–797
DOI: https://doi.org/10.1007/s10958-017-3266-y
Document Type: Article
UDC: 512.543
Language: Russian
Citation: V. G. Bardakov, M. S. Petukhova, “On potential counterexamples to the problem of zero divisors”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 30–50; J. Math. Sci., 221:6 (2017), 778–797
Citation in format AMSBIB
\Bibitem{BarPet15}
\by V.~G.~Bardakov, M.~S.~Petukhova
\paper On potential counterexamples to the problem of zero divisors
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2015
\vol 15
\issue 3
\pages 30--50
\mathnet{http://mi.mathnet.ru/vngu374}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 221
\issue 6
\pages 778--797
\crossref{https://doi.org/10.1007/s10958-017-3266-y}
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  • https://www.mathnet.ru/eng/vngu/v15/i3/p30
    • 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
    		Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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    References:84
    First page:35
     
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