Smoktunowicz–Bell conjecture on prime monomial algebras

Let $A$ be a prime monomial algebra over a field $k$. A monomial algebra is an algebra of the form

$$A\cong k\{x_1,\ldots,x_d\}/I,$$

where $I$ is generated by monomials in $x_1,\ldots,x_d$.

Smoktunowicz–Bell conjecture. Every prime monomial algebra $A$ is either PI, primitive, or has nonzero Jacobson radical.

The conjecture concerns the possible structure of prime monomial algebras. The paper proves a special case for finitely presented monomial algebras, and more generally for automaton algebras, but the full statement is not resolved in the supplied source.