Polynomial Identities in Algebras, Di Vincenzo Onofrio Mario, Giambruno Antonio

Автор: Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff
Название: Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
ISBN: 1470451743 ISBN-13(EAN): 9781470451745
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 82770.00 T
Наличие на складе: Поставка под заказ.
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: 158380.00 T
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: 65320.00 T
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: 63280.00 T
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.

Автор: Li Huishi
Название: Noncommutative Polynomial Algebras of Solvable Type and Their Modules: Basic Constructive-Computational Theory and Methods
ISBN: 1032079886 ISBN-13(EAN): 9781032079882
Издательство: Taylor&Francis
Рейтинг:
Цена: 163330.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
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: 121440.00 T
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: 90330.00 T
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: 83810.00 T
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: 111790.00 T
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: David A. Cox
Название: Applications of Polynomial Systems
ISBN: 1470451379 ISBN-13(EAN): 9781470451370
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 49330.00 T
Наличие на складе: Поставка под заказ.
Описание: Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert.Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bezier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century.The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.

Автор: Teo Mora
Название: Solving Polynomial Equation Systems I
ISBN: 0521811546 ISBN-13(EAN): 9780521811545
Издательство: Cambridge Academ
Рейтинг:
Цена: 183750.00 T
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: 182690.00 T
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.