Selected Works of A.I. Shirshov

  • Leonid Bokut
  • Ivan Shestakov
  • Victor Latyshev
  • Efim Zelmanov

Part of the Contemporary Mathematicians book series (CM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Publications of A.I. Shirshov

    1. Front Matter
      Pages 1-1
    2. A. I. Shirshov
      Pages 3-13
    3. A. I. Shirshov
      Pages 27-46
    4. A. I. Shirshov
      Pages 47-54
    5. A. I. Shirshov
      Pages 69-75
    6. A. I. Shirshov
      Pages 77-87
    7. A. I. Shirshov
      Pages 89-91
    8. A. I. Shirshov
      Pages 113-118
    9. A.I. Shirshov
      Pages 119-124
    10. A. I. Shirshov
      Pages 125-130
    11. A. I. Shirshov
      Pages 131-135
    12. A. I. Shirshov
      Pages 137-147
    13. A. I. Shirshov
      Pages 149-152
    14. A. I. Shirshov
      Pages 156-159
    15. A. I. Shirshov, A. A. Nikitin
      Pages 161-182
  3. Commentaries

    1. Front Matter
      Pages 183-183
    2. Alexei Belov-Kanel, Louis H. Rowen
      Pages 185-202
    3. Leonid A. Bokut
      Pages 203-215
    4. Vladislav K. Kharchenko
      Pages 217-221
    5. Alexander Kemer
      Pages 223-229
    6. Ivan Shestakov, Efim Zelmanov
      Pages 231-238
    7. Evgenii N. Kuzmin
      Pages 239-240
  4. Back Matter
    Pages 241-242

About this book


This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (1921–1981). He was a pioneer in several directions of associative, Lie, Jordan, and alternative algebras, as well as groups and projective planes. His name is associated with notions and results on Gröbner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshov’s Height Theorem, Lyndon-Shirshov words, Hall-Shirshov bases, Shirshov’s theorem on the Kurosh problem for alternative and Jordan algebras, and Shirshov’s theorem on the speciality of Jordan algebras with two generators. Shirshov’s ideas were used by his student Efim Zelmanov for the solution of the Restricted Burnside Problem. Several famous algebraists provide in this book detailed comments on the impact of Shirshov’s work on current algebra.


Lie Lie algebra Shirshov, Anatolii Illarionovich algebra theorem

Editors and affiliations

  • Leonid Bokut
    • 1
  • Ivan Shestakov
    • 2
  • Victor Latyshev
    • 3
  • Efim Zelmanov
    • 4
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.IME-USP Ruodo MataoSao PauloBrasil
  3. 3.Mehmat MGU im. LomonosovaMoscowRussia
  4. 4.Dep. of MathematicsUCSDLa JollaUSA

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