OpenAI · 196-01 · 2026-09-23 · Algebra
A Torsion-Free Group Algebra with Zero Divisors
preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026
Family 196. A counterexample to Kaplansky's zero-divisor conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Constructs a finitely presented torsion-free group whose group algebra has nonzero zero divisors, disproving Kaplansky's zero-divisor conjecture. The group has a finite two-dimensional classifying space.
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.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 196: A counterexample to Kaplansky’s zero-divisor conjecture. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.