Описание: A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Автор: Di Vincenzo Onofrio Mario, Giambruno Antonio Название: Polynomial Identities in Algebras ISBN: 3030631109 ISBN-13(EAN): 9783030631109 Издательство: Springer Цена: 20733.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems.
Автор: Kanel-Belov, Alexei , Karasik, Yakov , Rowen, Lo Название: Computational Aspects of Polynomial Identities ISBN: 0367445808 ISBN-13(EAN): 9780367445805 Издательство: Taylor&Francis Рейтинг: Цена: 10411.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. It gives all the details involved in Kemer`s proof of Specht`s conjecture for affine PI-algebras in characteristic 0. This edition presents a tighter formulation of Zubrilin`s theory and contains a more
Автор: Kanel-Belov, Alexei , Rowen, Louis Halle Название: Computational Aspects of Polynomial Identities ISBN: 0367446502 ISBN-13(EAN): 9780367446505 Издательство: Taylor&Francis Рейтинг: Цена: 10104.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces polynomial identity (PI)-algebras and reviews some well-known results and techniques, most of which are associated with the structure theory. It presents a full proof of Kemer`s solution to Specht`s conjecture.
Описание: This is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. This book is perfectly suited to researchers and postgrads researching noncommutative computational algebra.
Автор: Mora Название: Solving Polynomial Equation Systems III ISBN: 0521811554 ISBN-13(EAN): 9780521811552 Издательство: Cambridge Academ Рейтинг: Цена: 18216.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This third volume of four describes all the most important techniques, mainly based on Groebner bases. It covers the `standard` solutions (Gianni-Kalkbrener, Auzinger-Stetter, Cardinal-Mourrain) as well as the more innovative (Lazard-Rouillier, Giusti-Heintz-Pardo). The author also explores the historical background, from Bezout to Macaulay.
Автор: Franz Winkler Название: Polynomial Algorithms in Computer Algebra ISBN: 3211827595 ISBN-13(EAN): 9783211827598 Издательство: Springer Рейтинг: Цена: 11825.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers an introduction to the mathematical underpinnings of computer algebra. This book treats subjects that range from arithmetic of integers and polynomials to fast factorization methods, Grobner bases, and algorithms in algebraic geometry. It is suitable for both mathematics and computer science students.
Автор: Alicia Dickenstein; Ioannis Z. Emiris Название: Solving Polynomial Equations ISBN: 3642063616 ISBN-13(EAN): 9783642063619 Издательство: Springer Рейтинг: Цена: 10971.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Arno van den Essen Название: Polynomial Automorphisms ISBN: 3034895674 ISBN-13(EAN): 9783034895675 Издательство: Springer Рейтинг: Цена: 14635.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest.
Автор: Teo Mora Название: Solving Polynomial Equation Systems I ISBN: 0521811546 ISBN-13(EAN): 9780521811545 Издательство: Cambridge Academ Рейтинг: Цена: 27562.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Автор: Mora Название: Solving Polynomial Equation Systems IV ISBN: 1107109639 ISBN-13(EAN): 9781107109636 Издательство: Cambridge Academ Рейтинг: Цена: 27403.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this fourth and final volume the author covers extensions of Buchberger`s Algorithm, including a discussion of the most promising recent alternatives to Groebner bases: Gerdt`s involutive bases and Faugere`s F4 and F5 algorithms. This completes the author`s comprehensive treatise, which is a fundamental reference for any mathematical library.
Описание: - The Shestakov-Umirbaev Theory and Nagata's Conjecture. - Counterexamples to Hilbert's Fourteenth Problem. - Prime Characteristic Methods and the Cancellation Problem. - The Jacobian Conjecture: New Equivalences. - Mathieu-Zhao Spaces.
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