OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Constructs a finitely presented torsion-free group G whose group algebra \mathbb F_2[G] has nonzero zero divisors, disproving Kaplansky's zero-divisor conjecture. The group has a finite two-dimensional classifying space.
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We disprove Kaplansky's zero-divisor conjecture by constructing a finitely presented torsion-free group G for which \mathbb F_2[G] has nonzero zero divisors. The group admits a finite two-dimensional classifying space.
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