A counterexample to Kurosh's division-ring problem at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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A counterexample to Kurosh's division-ring problem

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Skills:	multiplying things	Levels:	1
Category:	Algebra	Lean version:	not yet
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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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LEVEL 1 A Counterexample to Kurosh’s Division-Ring Problem

released 2026-09-23 | 3 theorems · 20 lemmas · 28 proofs · 20,321 words | PLAY LEVEL 1 » (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.

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