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arxiv: 0911.4214 · v1 · submitted 2009-11-22 · 🧮 math.RA

A dichotomy result for prime algebras of Gelfand-Kirillov dimension two

classification 🧮 math.RA
keywords primeaffirmativealgebraalgebrasansweringdichotomydimensioneither
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Let $k$ be an uncountable field. We show that a finitely generated prime Goldie $k$-algebra of quadratic growth is either primitive or satisfies a polynomial identity, answering a question of Small in the affirmative.

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