Abstract
Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.
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Smoktunowicz, A. Centers in domains with quadratic growth. centr.eur.j.math. 3, 644–653 (2005). https://doi.org/10.2478/BF02475624
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DOI: https://doi.org/10.2478/BF02475624