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A counterexample to Kurosh’s division-ring problem
Constructs a countable characteristic-zero division ring that is algebraic over its center and generated by two elements over that center, but has infinite dimension over it. This answers Kurosh's division-ring problem on local finiteness negatively.
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A Counterexample to Kurosh’s Division-Ring Problem
Sep 23, 2026·paper.pdf
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.