Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras
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Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras
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Author : Eli Aljadeff
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-14
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras written by Eli Aljadeff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Education categories.
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.
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras
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Author : Eli Aljadeff
language : en
Publisher:
Release Date : 2020
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras written by Eli Aljadeff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with PI-algebras categories.
Polynomial Identities In Algebras
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Author : Onofrio Mario Di Vincenzo
language : en
Publisher: Springer Nature
Release Date : 2021-03-22
Polynomial Identities In Algebras written by Onofrio Mario Di Vincenzo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-22 with Mathematics categories.
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 Identities In Ring Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1980-07-24
Polynomial Identities In Ring Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-07-24 with Mathematics categories.
Polynomial Identities in Ring Theory
Amitsur Centennial Symposium
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Author : Avinoam Mann
language : en
Publisher: American Mathematical Society, Bar-Ilan University
Release Date : 2024-05-14
Amitsur Centennial Symposium written by Avinoam Mann and has been published by American Mathematical Society, Bar-Ilan University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-14 with Mathematics categories.
This volume contains the proceedings of the Amitsur Centennial Symposium, held from November 1–4, 2021, virtually and at the Israel Institute for Advanced Studies (IIAS), The Hebrew University of Jerusalem, Jerusalem, Israel. Shimshon Amitsur was a pioneer in several branches of algebra, the leading algebraist in Israel for several decades who contributed major theorems, inspiring results, useful observations, and enlightening tricks to many areas of the field. The fifteen papers included in the volume represent the broad impact of Amitsur's work on such areas as the theory of finite simple groups, algebraic groups, PI-algebras and growth of rings, quadratic forms and division algebras, torsors and Severi-Brauer surfaces, Hopf algebras and braces, invariants, automorphisms and derivations.
The Invariant Theory Of Matrices
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Author : Corrado De Concini
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-16
The Invariant Theory Of Matrices written by Corrado De Concini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Mathematics categories.
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.
Polynomial Identity Rings
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Author : Vesselin Drensky
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Polynomial Identity Rings written by Vesselin Drensky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity. These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity. 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. The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory.
Brauer Groups In Ring Theory And Algebraic Geometry
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Author : F. van Oystaeyen
language : en
Publisher: Springer
Release Date : 2006-11-14
Brauer Groups In Ring Theory And Algebraic Geometry written by F. van Oystaeyen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Computational Aspects Of Polynomial Identities
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Author : Alexei Kanel-Belov
language : en
Publisher: CRC Press
Release Date : 2005-02-22
Computational Aspects Of Polynomial Identities written by Alexei Kanel-Belov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-22 with Mathematics categories.
A comprehensive study of the main research done in polynomial identities over the last 25 years, including Kemer's solution to the Specht problem in characteristic O and examples in the characteristic p situation. The authors also cover codimension theory, starting with Regev's theorem and continuing through the Giambruno-Zaicev exponential rank. T
Methods In Ring Theory
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Author : Vesselin Drensky
language : en
Publisher: CRC Press
Release Date : 2021-02-27
Methods In Ring Theory written by Vesselin Drensky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-27 with Mathematics categories.
"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."