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Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras
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Book Synopsis Rings with Polynomial Identities and Finite Dimensional Representations of Algebras by : Eli Aljadeff
Download or read book Rings with Polynomial Identities and Finite Dimensional Representations of Algebras written by Eli Aljadeff and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rings with Polynomial Identities by : Claudio Procesi
Download or read book Rings with Polynomial Identities written by Claudio Procesi and published by . This book was released on 1973 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polynomial Identities in Algebras by : Onofrio Mario Di Vincenzo
Download or read book Polynomial Identities in Algebras written by Onofrio Mario Di Vincenzo and published by Springer Nature. This book was released on 2021-03-22 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Polynomial Identity Rings by : Vesselin Drensky
Download or read book Polynomial Identity Rings written by Vesselin Drensky and published by Birkhäuser. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Polynomial Identities in Ring Theory by :
Download or read book Polynomial Identities in Ring Theory written by and published by Academic Press. This book was released on 1980-07-24 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial Identities in Ring Theory
Book Synopsis Identities of Algebras and their Representations by : I︠U︡riĭ Pitrimovich Razmyslov
Download or read book Identities of Algebras and their Representations written by I︠U︡riĭ Pitrimovich Razmyslov and published by American Mathematical Soc.. This book was released on 1994 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and *a-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and *a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.
Book Synopsis Polynomial Identities and Asymptotic Methods by : A. Giambruno
Download or read book Polynomial Identities and Asymptotic Methods written by A. Giambruno and published by American Mathematical Society(RI). This book was released on 2014-05-21 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a state of the art approach to the study of polynomial identities satisfied by a given algebra by combining methods of ring theory, combinatorics, and representation theory of groups with analysis. The idea of applying analytical methods to the theory of polynomial identities appeared in the early 1970s and this approach has become one of the most powerful tools of the theory. A PI-algebra is any algebra satisfying at least one nontrivial polynomial identity. This includes the polynomial rings in one or several variables, the Grassmann algebra, finite-dimensional algebras, and many other algebras occurring naturally in mathematics. The core of the book is the proof that the sequence of co-dimensions of any PI-algebra has integral exponential growth - the PI-exponent of the algebra. Later chapters further apply these results to subjects such as a characterization of varieties of algebras having polynomial growth and a classification of varieties that are minimal for a given exponent.
Book Synopsis Noncommutative Rings by : I. N. Herstein
Download or read book Noncommutative Rings written by I. N. Herstein and published by Cambridge University Press. This book was released on 2005-09-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject.
Book Synopsis Methods in Ring Theory by : Vesselin Drensky
Download or read book Methods in Ring Theory written by Vesselin Drensky and published by CRC Press. This book was released on 1998-03-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Author :Avinoam Mann Publisher :American Mathematical Society, Bar-Ilan University ISBN 13 :1470475553 Total Pages :322 pages Book Rating :4.4/5 (74 download)
Book Synopsis Amitsur Centennial Symposium by : Avinoam Mann
Download or read book Amitsur Centennial Symposium written by Avinoam Mann and published by American Mathematical Society, Bar-Ilan University. This book was released on 2024-05-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Invariant Theory of Matrices by : Corrado De Concini
Download or read book The Invariant Theory of Matrices written by Corrado De Concini and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Some Aspects of Ring Theory by : I. N. Herstein
Download or read book Some Aspects of Ring Theory written by I. N. Herstein and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: S. Amitsur: Associative rings with identities.- I.N. Herstein: Topics in ring theory.- N. Jacobson: Representation theory of Jordan algebras.- I. Kaplansky: The theory of homological dimension.- D. Buchsbaum: Complexes in local ring theory.- P.H. Cohn: Two topics in ring theory.- A.W. Goldie: Non-commutative localisation.
Book Synopsis Algebras, Rings And Their Representations - Proceedings Of The International Conference On Algebras, Modules And Rings by : Alberto Facchini
Download or read book Algebras, Rings And Their Representations - Proceedings Of The International Conference On Algebras, Modules And Rings written by Alberto Facchini and published by World Scientific. This book was released on 2006-02-20 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories.The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith.
Book Synopsis Groups, Rings, and Group Rings by : A. Giambruno
Download or read book Groups, Rings, and Group Rings written by A. Giambruno and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28-August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed."--Publisher's website.
Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Book Synopsis Algebraists' Homage by : Shimshon A. Amitsur
Download or read book Algebraists' Homage written by Shimshon A. Amitsur and published by American Mathematical Soc.. This book was released on 1982 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Brauer Groups in Ring Theory and Algebraic Geometry by : F. van Oystaeyen
Download or read book Brauer Groups in Ring Theory and Algebraic Geometry written by F. van Oystaeyen and published by Springer. This book was released on 2006-11-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
