This book contains two contributions: "Combinatorial and Asymptotic Methods in Algebra" by V.A. Ufnarovskij is a survey of various combinatorial methods in infinite-dimensional algebras, widely interpreted to contain homological algebra and vigorously developing computer algebra, and narrowly interpreted as the study of algebraic objects defined by generators and their relations. The author shows how objects like words, graphs and automata provide valuable information in asymptotic studies. The main methods emply the notions of Gröbner bases, generating functions, growth and those of homological algebra. Treated are also problems of relationships between different series, such as Hilbert, Poincare and Poincare-Betti series. Hyperbolic and quantum groups are also discussed. The reader does not need much of background material for he can find definitions and simple properties of the defined notions introduced along the way. "Non-Associative Structures" by E.N.Kuz'min and I.P.Shestakov surveys the modern state of the theory of non-associative structures that are nearly associative. Jordan, alternative, Malcev, and quasigroup algebras are discussed as well as applications of these structures in various areas of mathematics and primarily their relationship with the associative algebras. Quasigroups and loops are treated too. The survey is self-contained and complete with references to proofs in the literature. The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics.
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Text: English (translation)
Original Language: Russian --This text refers to an out of print or unavailable edition of this title.
Original Language: Russian --This text refers to an out of print or unavailable edition of this title.
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5.0 out of 5 stars
one of the best books about Combinatorial Methods,
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This review is from: Algebra VI: Combinatorial and Asymptotic Methods of Algebra: Non-Associative Structures (Encyclopaedia of Mathematical Sciences) (Hardcover)
I found all what I need in the book. Very interesting discussion of ideas in different areas of algebra.
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Notes Math, Algebra Logic, Algebra Logika, Pure Appl, Itogi Nauki Tekh, Berlin-Heidelberg-New York, Academic Press, London Math, Malcev A-module, Notes Comput, Steklov Inst, Z-graded Lie Browse Sample Pages:
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Notes Math, Algebra Logic, Algebra Logika, Pure Appl, Itogi Nauki Tekh, Berlin-Heidelberg-New York, Academic Press, London Math, Malcev A-module, Notes Comput, Steklov Inst, Z-graded Lie Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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- Around Burnside (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge) by A. I. Kostrikin on page 189, and Back Matter
- Lie Algebras (Dover Books on Mathematics) by Nathan Jacobson on page 188, and page 235
- Homological Algebra by S.I. Gelfand on page 22, and page 186
- Infinite Dimensional Lie Superalgebras (De Gruyter Expositions in Mathematics) by Yuri A. Bahturin on page 194
- Combinatorial Theory (Wiley Classics Library) by Marshall Hall on page 187
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