Must a finitely presented nil algebra be nilpotent? (Ufnarovskij's question)
Claims Corollary 3.8: there is an infinite-dimensional finitely presented nonunital associative -algebra that is nil and Jacobson radical but not nilpotent; its unitization is finitely presented, algebraic and infinite-dimensional. This answers Ufnarovskij's nil question, Amitsur's radical question and the finite-presentation version of Kurosh's algebraic finiteness question negatively, over . Every matrix over its positive-degree ideal is nilpotent. It does NOT give examples over other fields or in characteristic zero, and nilpotence indices are unbounded.
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Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Must a finitely presented nil algebra be nilpotent? (Ufnarovskij's question) · Finitely presented nil algebras
Confidence: Not scored
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Companion: An infinite finitely presented residually finite 2-group evidence for this event
VibeMathed record: Must a finitely presented nil algebra be nilpotent? (Ufnarovskij's question) evidence for this event
Must a finitely presented nil algebra be nilpotent? (Ufnarovskij's question) parent of this event
Claims Corollary 3.8: there is an infinite-dimensional finitely presented nonunital associative -algebra that is nil and Jacobson radical but not nilpotent; its unitization is finitely presented, algebraic and infinite-dimensional. This answers Ufnarovskij's nil question, Amitsur's radical question and the finite-presentation version of Kurosh's algebraic finiteness question negatively, over . Every matrix over its positive-degree ideal is nilpotent. It does NOT give examples over other fields or in characteristic zero, and nilpotence indices are unbounded. parent of this event
The finitely presented Burnside problem: is every finitely presented periodic group finite? evidence for this event
Smoktunowicz (2008), The Jacobson radical of rings with nilpotent homogeneous elements evidence for this event
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