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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In A Counterexample to Kurosh’s Division-Ring Problem, 23 September 2026
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There is a countable division ring D of characteristic zero, with center F=Z(D), and elements x,y\in D such that
while every element of D is algebraic over F.
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Theorem 1.1
In A Counterexample to Kurosh’s Division-Ring Problem, 23 September 2026