On some Nonassociative Nil-rings and Algebraic Algebras
In the works of Levitzki  and Jacobson  devoted to the solution of the problem of Kurosh , 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 , but already Lie algebras give an example showing that the problem does not have a positive solution for arbitrary power associative algebras.
KeywordsInductive Hypothesis Additive Group Associative Algebra Jordan Algebra Associative Ring
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