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

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