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A counterexample to Kaplansky’s zero-divisor conjecture
Constructs a finitely presented torsion-free group G whose group algebra has nonzero zero divisors, disproving Kaplansky's zero-divisor conjecture. The group has a finite two-dimensional classifying space.
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A Torsion-Free Group Algebra with Zero Divisors
Sep 23, 2026·paper.pdfLean
We disprove Kaplansky's zero-divisor conjecture by constructing a finitely presented torsion-free group G for which has nonzero zero divisors. The group admits a finite two-dimensional classifying space.