Abstract
In the works of Levitzki [5] and Jacobson [3] devoted to the solution of the problem of Kurosh [4], it is proved that any associative algebraic algebra of bounded degree is locally finite, and that every associative nil-ring of bounded index is locally nilpotent. The problem of Kurosh can be stated for any class of power associative algebras [1], but already Lie algebras give an example showing that the problem does not have a positive solution for arbitrary power associative algebras.
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Shirshov, A.I. (2009). On some Nonassociative Nil-rings and Algebraic Algebras. In: Bokut, L., Shestakov, I., Latyshev, V., Zelmanov, E. (eds) Selected Works of A.I. Shirshov. Contemporary Mathematicians. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8858-4_6
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DOI: https://doi.org/10.1007/978-3-7643-8858-4_6
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