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Springer Monographs in Mathematics

Combinatorial Algebra: Syntax and Semantics

Authors: Sapir, Mark V.

  • 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
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eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-08031-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-08030-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: August 31, 2016
  • ISBN 978-3-319-37590-8
  • Free shipping for individuals worldwide
About this Textbook

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 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 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 t

he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.

About the authors

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

Reviews

“This book concentrates on the following three topics: the Burnside problem, the finite basis property and growth of algebras. … this book is a very valuable addition to the mathematical literature. … shows that there are ‘universal’ methods which can be used to investigate many algebraic problems from different parts of algebra … . it should also be noted that the book presents self-contained proofs of important recent results which were available only in research articles till now.” (Konrad P. Pióro, Mathematical Reviews, July, 2015)

“The book explores connections and interactions between ‘semantics’ (that is, ‘objects’ like graphs, topological spaces, etc.) and ‘syntactics’ (i.e. the means to speak about objects like words, laws, etc.) which occur in the analysis of algebraic structures. … The book … is addressed to active readers of a certain level of mathematical maturity. Included are more than 350 exercises and a collection of open problems.” (K. Auinger, Monatshefte für Mathematik, 2015)

“The book should be viewed as an encyclopedia of algebraic facts which have strong combinatorial flavor both in their statement and in proofs. … The book should be of interest to different audiences who want to be introduced to the fascinating world of combinatorial algebra, ranging from undergraduate students to senior scientists.” (Vadim Gorin, zbMATH 1319.05001, 2015)


Table of contents (5 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-08031-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-08030-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: August 31, 2016
  • ISBN 978-3-319-37590-8
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorial Algebra: Syntax and Semantics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-319-08031-4
DOI
10.1007/978-3-319-08031-4
Hardcover ISBN
978-3-319-08030-7
Softcover ISBN
978-3-319-37590-8
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVI, 355
Number of Illustrations and Tables
66 b/w illustrations
Topics