Polynomial Identities in Algebras

Polynomial Identities in Algebras
Title Polynomial Identities in Algebras PDF eBook
Author Onofrio Mario Di Vincenzo
Publisher Springer Nature
Pages 421
Release 2021-03-22
Genre Mathematics
ISBN 3030631117

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This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.

Polynomial Identity Rings

Polynomial Identity Rings
Title Polynomial Identity Rings PDF eBook
Author Vesselin Drensky
Publisher Birkhäuser
Pages 197
Release 2012-12-06
Genre Mathematics
ISBN 3034879342

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These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.

RINGS WITH POLYNOMIAL IDENTITIES AND FINITE DIMENSIONAL REPRESENTATIONS OF Algebras

RINGS WITH POLYNOMIAL IDENTITIES AND FINITE DIMENSIONAL REPRESENTATIONS OF Algebras
Title RINGS WITH POLYNOMIAL IDENTITIES AND FINITE DIMENSIONAL REPRESENTATIONS OF Algebras PDF eBook
Author Eli Aljadeff
Publisher
Pages
Release 2020
Genre PI-algebras
ISBN 9781470456955

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Rings with Polynomial Identities

Rings with Polynomial Identities
Title Rings with Polynomial Identities PDF eBook
Author Claudio Procesi
Publisher
Pages 232
Release 1973
Genre Mathematics
ISBN

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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras

Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
Title Rings with Polynomial Identities and Finite Dimensional Representations of Algebras PDF eBook
Author Eli Aljadeff
Publisher American Mathematical Soc.
Pages 630
Release 2020-12-14
Genre Education
ISBN 1470451743

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A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A 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.

Polynomial Identities in Ring Theory

Polynomial Identities in Ring Theory
Title Polynomial Identities in Ring Theory PDF eBook
Author
Publisher Academic Press
Pages 387
Release 1980-07-24
Genre Mathematics
ISBN 0080874002

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Polynomial Identities in Ring Theory

A Polynomial Approach to Linear Algebra

A Polynomial Approach to Linear Algebra
Title A Polynomial Approach to Linear Algebra PDF eBook
Author Paul A. Fuhrmann
Publisher Springer Science & Business Media
Pages 368
Release 2012-10-01
Genre Mathematics
ISBN 1441987347

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A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.