On Zero Divisors with Small Support in Group Rings of Torsion-Free Groups

@article{Schweitzer2012OnZD,
title={On Zero Divisors with Small Support in Group Rings of Torsion-Free Groups},
author={Pascal Schweitzer},
journal={CoRR},
year={2012},
volume={abs/1202.6645}
}

Kaplanski’s Zero Divisor Conjecture envisions that for a torsion-free group G and an integral domain R, the group ring R[G] does not contain non-trivial zero divisors. We define the length of an element α ∈ R[G] as the minimal non-negative integer k for which there are ring elements r1, . . . , rk ∈ R and group elements g1, . . . , gk ∈ G such that α = r1g1 + . . .+ rkgk. We investigate the conjecture when R is the field of rational numbers. By a reduction to the finite field with two elements… CONTINUE READING