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arXiv · 1102.2697

On a conjecture of Goodearl: Jacobson radical non-nil algebras of Gelfand-Kirillov dimension 2

Agata Smoktunowicz·Laurent Bartholdi
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Abstract

For an arbitrary countable field, we construct an associative algebra that is graded, generated by finitely many degree-1 elements, is Jacobson radical, is not nil, is prime, is not PI, and has Gelfand-Kirillov dimension two. This refutes a conjecture attributed to Goodearl.

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Agata Smoktunowicz, Laurent Bartholdi. 2011-02-14. On a conjecture of Goodearl: Jacobson radical non-nil algebras of Gelfand-Kirillov dimension 2. https://doi.org/10.1007/s11856-012-0073-5

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