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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras, Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff


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Автор: Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff
Название:  Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
ISBN: 9781470451745
Издательство: Mare Nostrum (Eurospan)
Классификация:


ISBN-10: 1470451743
Обложка/Формат: Paperback
Страницы: 630
Вес: 1.34 кг.
Дата издания: 30.12.2020
Серия: Colloquium publications
Язык: English
Размер: 187 x 265 x 43
Ключевые слова: Algebra,Algebraic geometry
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Поставляется из: Англии
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 Shirshovs 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. Artins 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.
Дополнительное описание: Algebra|Algebraic geometry



Handbook Of The Tutte Polynomial

Название: Handbook Of The Tutte Polynomial
ISBN: 1482240629 ISBN-13(EAN): 9781482240627
Издательство: Taylor&Francis
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Цена: 32921.00 р.
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Описание: This is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters, written by experts in the field, that collectively offer a concise overview of the polynomial`s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial.

Solving Polynomial Equation Systems III

Автор: Mora
Название: Solving Polynomial Equation Systems III
ISBN: 0521811554 ISBN-13(EAN): 9780521811552
Издательство: Cambridge Academ
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Цена: 18216.00 р.
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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.

Computational Aspects of Polynomial Identities

Автор: Kanel-Belov, Alexei , Karasik, Yakov , Rowen, Lo
Название: Computational Aspects of Polynomial Identities
ISBN: 0367445808 ISBN-13(EAN): 9780367445805
Издательство: Taylor&Francis
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Цена: 9798.00 р.
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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

Computational Aspects of Polynomial Identities

Автор: Kanel-Belov, Alexei , Rowen, Louis Halle
Название: Computational Aspects of Polynomial Identities
ISBN: 0367446502 ISBN-13(EAN): 9780367446505
Издательство: Taylor&Francis
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Цена: 9492.00 р.
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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.

Polynomial Invariants of Finite Groups

Автор: Smith, Larry
Название: Polynomial Invariants of Finite Groups
ISBN: 0367449137 ISBN-13(EAN): 9780367449131
Издательство: Taylor&Francis
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Цена: 9798.00 р.
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Описание: This is a book about the invariant theory of finite groups, written by an algebraic topologist. It illustrates the theorems by applying them to concrete cases, and examines several basic ideas and problems of invariant theory in the context of some elementary examples.

Polynomial Rings and Affine Algebraic Geometry: Praag 2018, Tokyo, Japan, February 12-16

Автор: Kuroda Shigeru, Onoda Nobuharu, Freudenburg Gene
Название: Polynomial Rings and Affine Algebraic Geometry: Praag 2018, Tokyo, Japan, February 12-16
ISBN: 303042135X ISBN-13(EAN): 9783030421359
Издательство: Springer
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Цена: 19564.00 р.
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Описание: This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018.

Polynomial Completeness in Algebraic Systems

Автор: Kaarli, Kalle , Pixley, Alden F.
Название: Polynomial Completeness in Algebraic Systems
ISBN: 0367398338 ISBN-13(EAN): 9780367398330
Издательство: Taylor&Francis
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Цена: 9798.00 р.
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Описание:

Boolean algebras have historically played a special role in the development of the theory of general or universal algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra.

In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and systematically extends another specific property of Boolean algebras: the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them.

An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems.

Polynomial Algorithms in Computer Algebra

Автор: Franz Winkler
Название: Polynomial Algorithms in Computer Algebra
ISBN: 3211827595 ISBN-13(EAN): 9783211827598
Издательство: Springer
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Цена: 13549.00 р.
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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.

Polynomial Automorphisms

Автор: Arno van den Essen
Название: Polynomial Automorphisms
ISBN: 3034895674 ISBN-13(EAN): 9783034895675
Издательство: Springer
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Цена: 16769.00 р.
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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.

Polynomial Theory of Error Correcting Codes

Автор: Giovanni Cancellieri
Название: Polynomial Theory of Error Correcting Codes
ISBN: 3319378708 ISBN-13(EAN): 9783319378701
Издательство: Springer
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Цена: 22201.00 р.
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Описание: Numerous examples and indexed definitions make this detailed guide to polynomial theory in error-correcting codes a highly accessible resource. New codes and a unitary approach to block and convolutional codes will enhance readers` understanding of the topic.


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