| Description |
1 online resource (xvi, 355 pages) : illustrations |
| Series |
Springer Monographs in Mathematics, 1439-7382 |
|
Springer monographs in mathematics, 1439-7382
|
| Contents |
Introduction -- 1. Main definitions and basic fact -- 2. Words that can be avoided -- 3. Semigroups -- 4. Rings -- 5. Groups -- Bibliography -- Index |
| Summary |
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 Golod-Shafarevich 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, Bass-Guivarc'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 ù̀niversal" 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 zFurther reading and open problemsy sections at the end of Chapters 2 -5. The book can be used in a classroom and for self-study, engagin g anyone who wishes to learn and better understand this important area of mathematics |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
English |
|
Online resource; title from PDF title page (SpringerLink, viewed October 16, 2014) |
| In |
Springer eBooks |
| Subject |
Combinatorial analysis.
|
|
Combinatorial analysis
|
| Form |
Electronic book
|
| ISBN |
9783319080314 |
|
3319080318 |
|
331908030X |
|
9783319080307 |
|
