On some Nonassociative Nil-rings and Algebraic Algebras

  • A. I. Shirshov
Part of the Contemporary Mathematicians book series (CM)


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.


Inductive Hypothesis Additive Group Associative Algebra Jordan Algebra Associative Ring 
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© Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland 2009

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  • A. I. Shirshov

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