TY - JOUR

T1 - On Potential Counterexamples to the Problem of Zero Divisors

AU - Bardakov, V. G.

AU - Petukhova, M. S.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85011654077&partnerID=8YFLogxK

U2 - 10.1007/s10958-017-3266-y

DO - 10.1007/s10958-017-3266-y

M3 - Article

AN - SCOPUS:85011654077

VL - 221

SP - 778

EP - 797

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 6

ER -