Email this article On Potential Counterexamples to the Problem of Zero Divisors
- Authors: Bardakov V.G.1,2, Petukhova M.S.2
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Affiliations:
- Sobolev Institute of Mathematics SB RAS
- Novosibirsk State University
- Issue: Vol 221, No 6 (2017)
- Pages: 778-797
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239097
- DOI: https://doi.org/10.1007/s10958-017-3266-y
- ID: 239097
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Abstract
E. Rips constructed a series of groups such that their group rings have zero divisors. such groups can serve as counterexamples to Kaplansky’s problem on zero divisors. The problem is to find such a group without torsion. We study simplest groups of this series, classify such groups, describe the structure, and show that all such groups have 2-torsion.
About the authors
V. G. Bardakov
Sobolev Institute of Mathematics SB RAS; Novosibirsk State University
Author for correspondence.
Email: bardakov@math.nsc.ru
Russian Federation, 4, pr. Akad. Koptyuga, Novosibirsk, 630090; 2, ul. Pirogova, Novosibirsk, 630090
M. S. Petukhova
Novosibirsk State University
Email: bardakov@math.nsc.ru
Russian Federation, 2, ul. Pirogova, Novosibirsk, 630090
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