Selected Works of A.I. Shirshov [electronic resource] / edited by Leonid Bokut, Ivan Shestakov, Victor Latyshev, Efim Zelmanov.

Publications of A.I. Shirshov -- Subalgebras of Free Lie Algebras -- On the Representation of Lie Rings in Associative Rings -- Subalgebras of Free Commutative and Free Anticommutative Algebras -- On Special J-rings -- Some Theorems on Embedding of Rings -- On some Nonassociative Nil-rings and Algebraic Algebras -- On Rings with Identical Relations -- On Free Lie Rings -- On a Problem of Levitzki -- Some Problems in the Theory of Rings that are Nearly Associative -- On the Bases of a Free Lie Algebra -- Some Algorithmic Problems for ?-algebras -- Some Algorithmic Problems for Lie Algebras -- On a Hypothesis in the Theory of Lie Algebras -- On Some Groups which are Nearly Engel -- On Some Identical Relations for Algebras -- On Some Positively Definable Varieties of Groups -- On the Definition of the Binary-Lie Property -- On the Theory of Projective Planes -- Commentaries -- Perspectives on Shirshovs Height Theorem -- On Shirshovs Papers for Lie Algebras -- Some of A.I. Shirshovs works -- Comments on Shirshovs Height Theorem -- A.I. Shirshovs Works on Alternative and Jordan Algebras -- A Word about the Teacher.

This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (19211981). 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 Grȵbner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshovs Height Theorem, Lyndon-Shirshov words, Hall-Shirshov bases, Shirshovs theorem on the Kurosh problem for alternative and Jordan algebras, and Shirshovs theorem on the speciality of Jordan algebras with two generators. Shirshovs 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 Shirshovs work on current algebra.