{"id":"openai-math/A-Torsion-Free-Group-Algebra-with-Zero-Divisors","pdf":"https://github.com/openai/math/blob/main/preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Torsion-Free-Group-Algebra-with-Zero-Divisors-September-23-2026","tags":["group-theory","group-algebras","zero-divisors","kaplansky-conjecture"],"score":0,"title":"A Torsion-Free Group Algebra with Zero Divisors","domain":"Algebra","family":"196","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"A counterexample to Kaplansky’s zero-divisor conjecture"}