The Jacobian Conjecture, Together with Specht and Burnside-Type Problems

  • Alexei Belov
  • Leonid Bokut
  • Louis Rowen
  • Jie-Tai Yu
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 79)


We explore an approach to the celebrated Jacobian Conjecture by means of identities of algebras, initiated by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951–2001), whose works have only been partially published. This approach also indicates some very close connections between mathematical physics, universal algebra, and automorphisms of polynomial algebras.


Associative Algebra Jordan Algebra Algebraic Extension Prime Algebra Free Associative Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The first and third authors are supported by the Israel Science Foundation grant No. 1207/12. The research of Jie-Tai Yu was partially supported by an RGC-GRF Grant.

Yagzhev was a doctoral student of the second author, L. Bokut.

We thank I.P. Shestakov for useful comments, and also thank the referees for many helpful suggestions in improving the exposition.

We are grateful to Yagzhev’s widow G.I. Yagzheva, and also to Jean-Yves Sharbonel, for providing some unpublished materials.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexei Belov
    • 1
  • Leonid Bokut
    • 2
    • 3
  • Louis Rowen
    • 1
  • Jie-Tai Yu
    • 4
  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.South China Normal UniversityGuangzhouChina
  4. 4.Department of MathematicsThe University of Hong KongHong Kong SARChina

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