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Selected Works of A.I. Shirshov

  • Book
  • © 2009

Overview

Editors:
  1. Leonid Bokut

    1. Sobolev Institute of Mathematics, Novosibirsk, Russia

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  2. Ivan Shestakov

    1. IME-USP Ruodo Matao, Sao Paulo, Brasil

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  3. Victor Latyshev

    1. Mehmat MGU im. Lomonosova, Moscow, Russia

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  4. Efim Zelmanov

    1. Dep. of Mathematics, UCSD, La Jolla, USA

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  • English translations of Shirshov’s works, which were published only in Russian
  • Due to Shirshov's future leading and unique handling of algebraic problems, the results are still of high interest for current research in algebra
  • Includes supplementary material: sn.pub/extras

Part of the book series: Contemporary Mathematicians (CM)

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Publications of A.I. Shirshov

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Subalgebras of Free Lie Algebras

      • A. I. Shirshov
      Pages 3-13

    3. On the Representation of Lie Rings in Associative Rings

      • A. I. Shirshov
      Pages 15-17

    4. Subalgebras of Free Commutative and Free Anticommutative Algebras

      • A. I. Shirshov
      Pages 19-25

    5. On Special J-rings

      • A. I. Shirshov
      Pages 27-46

    6. Some Theorems on Embedding of Rings

      • A. I. Shirshov
      Pages 47-54

    7. On some Nonassociative Nil-rings and Algebraic Algebras

      • A. I. Shirshov
      Pages 55-68

    8. On Rings with Identical Relations

      • A. I. Shirshov
      Pages 69-75

    9. On Free Lie Rings

      • A. I. Shirshov
      Pages 77-87

    10. On a Problem of Levitzki

      • A. I. Shirshov
      Pages 89-91

    11. Some Problems in the Theory of Rings that are Nearly Associative

      • A. I. Shirshov
      Pages 93-111

    12. On the Bases of a Free Lie Algebra

      • A. I. Shirshov
      Pages 113-118

    13. Some Algorithmic Problems for ε-algebras

      • A.I. Shirshov
      Pages 119-124

    14. Some Algorithmic Problems for Lie Algebras

      • A. I. Shirshov
      Pages 125-130

    15. On a Hypothesis in the Theory of Lie Algebras

      • A. I. Shirshov
      Pages 131-135

    16. On Some Groups which are Nearly Engel

      • A. I. Shirshov
      Pages 137-147

    17. On Some Identical Relations for Algebras

      • A. I. Shirshov
      Pages 149-152

    18. On Some Positively Definable Varieties of Groups

      • A. I. Shirshov
      Pages 153-155

    19. On the Definition of the Binary-Lie Property

      • A. I. Shirshov
      Pages 156-159
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Keywords

About this book

Anatolii Illarionovich Shirshov (1921–1981) was an outstanding Russian mat- maticianwhoseworksessentiallyin?uenced thetheoriesofassociative,Lie,Jordan and alternative rings. Many Shirshov’s students and students of his students had a successful research career in mathematics. AnatoliiShirshovwasbornonthe8thofAugustof1921inthevillageKolyvan near Novosibirsk. Before the II World War he started to study mathematics at Tomsk university but then went to the front to ?ght as a volunteer. In 1946 he continued his study at Voroshilovgrad (now Lugansk) Pedagogical Institute and at the same time taught mathematics at a secondary school. In 1950 Shirshov was accepted as a graduate student at the Moscow State University under the supervision of A. G. Kurosh. In 1953 he has successfully defended his Candidate of Science thesis (analog of a Ph. D. ) “Some problems in the theory of nonassociative rings and algebras” and joined the Department of Higher Algebra at the Moscow State University. In 1958 Shirshov was awarded the Doctor of Science degree for the thesis “On some classes of rings that are nearly associative”. In 1960 Shirshov moved to Novosibirsk (at the invitations of S. L. Sobolev and A. I. Malcev) to become one of the founders of the new mathematical institute of the Academy of Sciences (now Sobolev Institute of Mathematics) and to help the formation of the new Novosibirsk State University. From 1960 to 1973 he was a deputy director of the Institute and till his last days he led the research in the theory of algebras at the Institute.

Editors and Affiliations

  • Sobolev Institute of Mathematics, Novosibirsk, Russia

    Leonid Bokut

  • IME-USP Ruodo Matao, Sao Paulo, Brasil

    Ivan Shestakov

  • Mehmat MGU im. Lomonosova, Moscow, Russia

    Victor Latyshev

  • Dep. of Mathematics, UCSD, La Jolla, USA

    Efim Zelmanov

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