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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, Volume 15, Issue 3, Pages 30–50 (Mi vngu374)  

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

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


Full text: PDF file (338 kB)
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English version:
Journal of Mathematical Sciences, 2017, 221:6, 778–797

UDC: 512.543
Received: 19.03.2015

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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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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