| Summary: | This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (1921<U+0013>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 Grb̲ner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshov<U+0019>s Height Theorem, Lyndon-Shirshov words, Hall-Shirshov bases, Shirshov<U+0019>s theorem on the Kurosh problem for alternative and Jordan algebras, and Shirshov<U+0019>s theorem on the speciality of Jordan algebras with two generators. Shirshov<U+0019>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<U+0019>s work on current algebra.
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