2 problems

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Smoktunowicz–Bell conjecture on prime monomial algebras
Smoktunowicz–Bell conjecture. Every prime monomial algebra $A$ is either PI, primitive, or has nonzero Jacobson radical.
Conjectureopenmonomial-algebras noncommutative-algebra primitive-algebrasarXiv posted 2 days ago
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Small's primitivity-or-PI conjecture for quadratic-growth algebras
Small's primitivity-or-PI conjecture. The algebra $A$ is either primitive or PI.
Conjectureopengrowth-of-algebras noncommutative-algebra primitive-algebrasarXiv posted 2 days ago

Smoktunowicz–Bell conjecture on prime monomial algebras