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Comments on Shirshov’s Height Theorem

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Selected Works of A.I. Shirshov

Part of the book series: Contemporary Mathematicians ((CM))

Abstract

In 1941 A.G. Kurosh [1] posed the problem: Is every finitely-generated algebraic associative algebra finite-dimensional? In 1964 E.S. Golod and I.R. Shafarevich 2, 3] constructed a counterexample: they presented an infinite-dimensional finitely-generated nil-algebra. This counterexample shows that in general finitelygenerated algebraic associative algebras are very far from being finite-dimensional.

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Authors
  1. Alexander Kemer
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Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyuga, 4, 630090, Novosibirsk, Russia

    Leonid Bokut

  2. IME-USP Ruodo Matao, 1010 Cidade Universitaria, CEP 05508-090, Sao Paulo, SP, Brasil

    Ivan Shestakov

  3. Mehmat MGU im. Lomonosova, Vorob’evy Gory, 119899, Moscow, Russia

    Victor Latyshev

  4. Dep. of Mathematics, UCSD, 9500 Gilman Drive #0112, La Jolla, CA, 92093-0112, USA

    Efim Zelmanov

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© 2009 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland

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Kemer, A. (2009). Comments on Shirshov’s Height Theorem. 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_23

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