Contemporary Mathematicians

# Selected Works of A.I. Shirshov

Editors: Bokut, L.A., Latyshev, V., Shestakov, I., Zelmanov, E. (Eds.)

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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 of his work are still of high interest for current research in algebra
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eBook $149.00 price for USA • ISBN 978-3-7643-8858-4 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Institutional customers should get in touch with their account manager Hardcover$189.00
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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.

• Subalgebras of Free Lie Algebras

Pages 3-13

Shirshov, A. I.

• On the Representation of Lie Rings in Associative Rings

Pages 15-17

Shirshov, A. I.

• Subalgebras of Free Commutative and Free Anticommutative Algebras

Pages 19-25

Shirshov, A. I.

• On Special J-rings

Pages 27-46

Shirshov, A. I.

• Some Theorems on Embedding of Rings

Pages 47-54

Shirshov, A. I.

eBook $149.00 price for USA • ISBN 978-3-7643-8858-4 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Institutional customers should get in touch with their account manager Hardcover$189.00
price for USA

## Bibliographic Information

Bibliographic Information
Book Title
Selected Works of A.I. Shirshov
Editors
• Leonid A. Bokut
• Victor Latyshev
• Ivan Shestakov
• Efim Zelmanov
Translated by
Bremner, M., Kotchetov, M.V.
Series Title
Contemporary Mathematicians
2009
Publisher
Birkhäuser Basel