Selected Works of A.I. Shirshov (eBook)

Leonid A. Bokut, Victor Latyshev, Ivan Shestakov, Efim Zelmanov (Herausgeber)

eBook Download: PDF

2009 | 2009
VII, 242 Seiten
Springer Basel (Verlag)
978-3-7643-8858-4 (ISBN)

Infos

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.

Inhalt

Contents 7
Preface 9
Publications of A.I. Shirshov 10
Subalgebras of Free Lie Algebras 11
On the Representation of Lie Rings in Associative Rings 22
Subalgebras of Free Commutative and Free Anticommutative Algebras 25
On Special J-rings 32
Some Theorems on Embedding of Rings 52
On some Nonassociative Nil-rings and Algebraic Algebras 60
On Rings with Identical Relations 74
On Free Lie Rings 81
On a Problem of Levitzki 92
Some Problems in the Theory of Rings that are Nearly Associative 95
On the Bases of a Free Lie Algebra 114
Some Algorithmic Problems for e-algebras 120
Some Algorithmic Problems for Lie Algebras 126
On a Hypothesis in the Theory of Lie Algebras 132
On Some Groups which are Nearly Engel 137
On Some Identical Relations for Algebras 148
On Some Positively Definable Varieties of Groups 152
On the Definition of the Binary-Lie Property 155
On the Theory of Projective Planes 158
Commentaries 180
Perspectives on Shirshov’s Height Theorem 181
On Shirshov’s Papers for Lie Algebras 199
Some of A.I. Shirshov’s Works 212
Comments on Shirshov’s Height Theorem 217
A.I. Shirshov’s Works on Alternative and Jordan Algebras 224
A Word about the Teacher 232
Indication of Sources 234

Produkt-Details

• Erscheint lt. Verlag: 9.11.2009
• Reihe/Serie: Contemporary Mathematicians
• Reihe/Serie: Contemporary Mathematicians
• Übersetzer: Murray Bremner, Mikhail V. Kotchetov
• Zusatzinfo: VII, 242 p.
• Verlagsort: Basel
• Sprache: englisch
• Original-Titel: 19 papers according to the enclosed list.
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Schlagworte: Algebra • Lie • Lie algebra • Shirshov, Anatolii Illarionovich • Theorem
• ISBN-10: 3-7643-8858-7 / 3764388587
• ISBN-13: 978-3-7643-8858-4 / 9783764388584