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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vngu374
https://www.mathnet.ru/eng/vngu/v15/i3/p30
This publication is cited in the following 2 articles:
Alireza Abdollahi, Fatemeh Jafari, “Cardinality of product sets in torsion-free groups and applications in group algebras”, J. Algebra Appl., 19:04 (2020), 2050079
Alireza Abdollahi, Fatemeh Jafari, “Zero divisor and unit elements with supports of size 4 in group algebras of torsion-free groups”, Communications in Algebra, 47:1 (2019), 424
Citation in format AMSBIB
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