{"id":"openai-math/A-Counterexample-to-Kuroshs-Division-Ring-Problem","pdf":"https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026","tags":["division-rings","algebra","kurosh-problem"],"score":0,"title":"A Counterexample to Kurosh’s Division-Ring Problem","domain":"Algebra","family":"201","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We construct a countable division ring of characteristic zero that is algebraic over its center, generated by two elements as an algebra over that center, and infinite-dimensional over it. This gives a negative answer to the Kurosh problem for division rings.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"A counterexample to Kurosh’s division-ring problem"}