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

  title={On Zero Divisors with Small Support in Group Rings of Torsion-Free Groups},
  author={Pascal Schweitzer},
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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On algorithmic problems in effectively complete classes of groups

  • S. I. Adyan
  • Dokl. Akad. Nauk SSSR, 123(1):13–16
  • 1958
Highly Influential
4 Excerpts

On the decidability of the zero-divisor problem

  • Ł. Grabowski
  • arXiv:1202.1162v1 [math.GR]
  • 2012
1 Excerpt

On the asphericity of length-6 relative presentations with torsion-free coefficients

  • S. K. Kim
  • Proc. Edinb. Math. Soc. (2), 51(1):201–214
  • 2008
1 Excerpt

An introduction to group rings

  • C. P. Milies, S. K. Sehgal
  • Algebras and Applications. Kluwer Academic…
  • 2002
1 Excerpt

Asphericity and zero divisors in group algebras

  • I. J. Leary
  • Journal of Algebra, 227(1):362 –364
  • 2000
1 Excerpt

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