Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 196-01. A Torsion-Free Group Algebra with Zero Divisors
Manuscript map · lines 5895–5904
OpenAI@2026-10-07#rem:oai-p-196-01
Authors: OpenAI. Family 196.
Title: A Torsion-Free Group Algebra with Zero Divisors.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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