A counterexample to the little finitistic-dimension conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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A counterexample to the little finitistic-dimension conjecture

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

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	multiplying things	Levels:	1
Category:	Algebra	Lean version:	YES! ✔
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A counterexample to finitistic-dimension finiteness. Constructs a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture.

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LEVEL 1 An algebra of infinite little finitistic dimension

released 2026-09-23 | 2 theorems · 7 lemmas · 16 proofs · 10,226 words | PLAY LEVEL 1 » (pdf)

We construct a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture.

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