| 书目名称 | Combinatorial Algebra: Syntax and Semantics | | 编辑 | Mark V. Sapir | | 视频video | http://file.papertrans.cn/230/229871/229871.mp4 | | 概述 | 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 th | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | .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 | | 出版日期 | Textbook 2014 | | 关键词 | Burnside-type problems; Novikov–Adian theorem; amenable groups; combinatorics on words; semigroups; symbo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-08031-4 | | isbn_softcover | 978-3-319-37590-8 | | isbn_ebook | 978-3-319-08031-4Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer International Publishing Switzerland 2014 |
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