Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes GolodShafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, BassGuivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the Further reading and open problems sections at the end of Chapters 2 5. The book can also be used for self-study, engaging those beyond the classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.

Contains proofs of more than 20 classical and modern results about Burnside properties, growth, finite basis property, automata, amenability, etc The book is self-contained; no prerequisites beyond the standard courses of linear and abstract algebra are required The book emphasizes common ideas and tools used in the proofs of various seemingly quite different theorems Includes supplementary material: sn.pub/extras

Autorentext
Mark V. Sapir is a Centennial Professor of Mathematics at Vanderbilt University.

Klappentext
Combinatorial Algebra: Syntax and Semantics provides a comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes GolodShafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, BassGuivarc'h theorem about the growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook,and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this book extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the Further reading and open problems sections at the end of Chapters 2 5. The book can be used in a classroom and for self-study, engaging anyone who wishes to learn and better understand this important area of mathematics.

Inhalt
Introduction.- 1. Main definitions and basic fact.- 2. Words that can be avoided.- 3. Semigroups.- 4. Rings.- 5. Groups.- Bibliography.- Index.