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Canad. Math. Bull., 2014, Volume 57, Issue 2, Pages 326–334 (Mi cmb1)  

On zero-divisors in group rings of groups with torsion

S. V. Ivanova, R. Mikhailovbc

a Department of Mathematics, University of Illinois at Urbana-Champaign
b Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia
c Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: Nontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.

Funding Agency Grant Number
National Science Foundation DMS 09-01782
Ministry of Education and Science of the Russian Federation 11.G34.31.0026
The first author is supported in part by NSF grant DMS 09-01782. This research of the second author is supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026.


DOI: https://doi.org/10.4153/CMB-2012-036-6


Bibliographic databases:

MSC: Primary 20C07; Secondary 20E06, 20F05, 20F50
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