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Combinatorial Algebra: Syntax and Semantics (Paperback, Softcover reprint of the original 1st ed. 2014)
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Combinatorial Algebra: Syntax and Semantics (Paperback, Softcover reprint of the original 1st ed. 2014)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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.
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