A Counterexample to Kurosh’s Division-Ring Problem
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.
Cite
@misc{OAI:A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026,
author = {{OpenAI}},
title = {{A Counterexample to Kurosh's Division-Ring Problem}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf}{OAI:A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026}},
year = {2026}
}