Associative Algebras

Download Associative Algebras full books in PDF, epub, and Kindle. Read online Associative Algebras ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Associative Algebras

Author : R.S. Pierce
Publisher : Springer Science & Business Media
ISBN 13 : 1475701632
Total Pages : 448 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis Associative Algebras by : R.S. Pierce

Download or read book Associative Algebras written by R.S. Pierce and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience. The material that is presented here should not be fatal if it is swallowed by persons who are not members of that group. The objects of our attention in this book are associative algebras, mostly the ones that are finite dimensional over a field. This subject is ideal for a textbook that will lead graduate students into a specialized field of research. The major theorems on associative algebras inc1ude some of the most splendid results of the great heros of algebra: Wedderbum, Artin, Noether, Hasse, Brauer, Albert, Jacobson, and many others. The process of refine ment and c1arification has brought the proof of the gems in this subject to a level that can be appreciated by students with only modest background. The subject is almost unique in the wide range of contacts that it makes with other parts of mathematics. The study of associative algebras con tributes to and draws from such topics as group theory, commutative ring theory, field theory, algebraic number theory, algebraic geometry, homo logical algebra, and category theory. It even has some ties with parts of applied mathematics.

Elements of the Representation Theory of Associative Algebras: Volume 1

Author : Ibrahim Assem
Publisher : Cambridge University Press
ISBN 13 : 9780521584234
Total Pages : 480 pages
Book Rating : 4.5/5 (842 download)

DOWNLOAD NOW!

Book Synopsis Elements of the Representation Theory of Associative Algebras: Volume 1 by : Ibrahim Assem

Download or read book Elements of the Representation Theory of Associative Algebras: Volume 1 written by Ibrahim Assem and published by Cambridge University Press. This book was released on 2006-02-13 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a two-volume set that provides a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. The treatment is self-contained and provides an elementary and up-to-date introduction to the subject using quiver-theoretical techniques and the theory of almost split sequences as well as tilting theory and the use of integral quadratic forms. Much of this material has never appeared before in book form. The book is primarily addressed to graduate students starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the ten chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study. Book jacket.

Associative and Non-Associative Algebras and Applications

Author : Mercedes Siles Molina
Publisher : Springer Nature
ISBN 13 : 3030352560
Total Pages : 338 pages
Book Rating : 4.0/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Associative and Non-Associative Algebras and Applications by : Mercedes Siles Molina

Download or read book Associative and Non-Associative Algebras and Applications written by Mercedes Siles Molina and published by Springer Nature. This book was released on 2020-01-02 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.

An Introduction to Nonassociative Algebras

Author : Richard D. Schafer
Publisher : Courier Dover Publications
ISBN 13 : 0486164179
Total Pages : 177 pages
Book Rating : 4.4/5 (861 download)

DOWNLOAD NOW!

Book Synopsis An Introduction to Nonassociative Algebras by : Richard D. Schafer

Download or read book An Introduction to Nonassociative Algebras written by Richard D. Schafer and published by Courier Dover Publications. This book was released on 2017-11-15 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise graduate-level introductory study presents some of the important ideas and results in the theory of nonassociative algebras. Places particular emphasis on alternative and (commutative) Jordan algebras. 1966 edition.

Representation Theory of Finite Groups and Associative Algebras

Author : Charles W. Curtis
Publisher : American Mathematical Soc.
ISBN 13 : 0821840665
Total Pages : 714 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Representation Theory of Finite Groups and Associative Algebras by : Charles W. Curtis

Download or read book Representation Theory of Finite Groups and Associative Algebras written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 2006 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.

Introduction to Octonion and Other Non-Associative Algebras in Physics

Author : Susumu Okubo
Publisher : Cambridge University Press
ISBN 13 : 0521472156
Total Pages : 152 pages
Book Rating : 4.5/5 (214 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Octonion and Other Non-Associative Algebras in Physics by : Susumu Okubo

Download or read book Introduction to Octonion and Other Non-Associative Algebras in Physics written by Susumu Okubo and published by Cambridge University Press. This book was released on 1995-08-03 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author aims to familiarize researchers and graduate students in both physics and mathematics with the application of non-associative algebras in physics.Topics covered by the author range from algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and YangSHBaxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and so on. Much of the material found in this book is not available in other standard works.

Linear Associative Algebras

Author : Alexander Abian
Publisher : Elsevier
ISBN 13 : 1483186792
Total Pages : 175 pages
Book Rating : 4.4/5 (831 download)

DOWNLOAD NOW!

Book Synopsis Linear Associative Algebras by : Alexander Abian

Download or read book Linear Associative Algebras written by Alexander Abian and published by Elsevier. This book was released on 2014-05-09 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems. The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors. The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix representation of algebras, and division of algebras. The manuscript also tackles the Wedderburn structure theorems, including direct sum and tensor product decomposition of algebras, nilpotent algebras and the radical of an algebra, and structure of simple and semi-simple algebras. The publication is highly recommended for mathematicians and students interested in the Wedderburn structure theorems and finite dimensional linear associative algebras.

Introduction to Representation Theory

Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

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.

Advanced Algebra

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
ISBN 13 : 0817646132
Total Pages : 757 pages
Book Rating : 4.8/5 (176 download)

DOWNLOAD NOW!

Book Synopsis Advanced Algebra by : Anthony W. Knapp

Download or read book Advanced Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.

Non-commutative Algebraic Geometry

Author : F.M.J. van Oystaeyen
Publisher : Springer
ISBN 13 : 3540386017
Total Pages : 408 pages
Book Rating : 4.5/5 (43 download)

DOWNLOAD NOW!

Book Synopsis Non-commutative Algebraic Geometry by : F.M.J. van Oystaeyen

Download or read book Non-commutative Algebraic Geometry written by F.M.J. van Oystaeyen and published by Springer. This book was released on 2006-11-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ideals of Identities of Associative Algebras

Author : Aleksandr Robertovich Kemer
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898291
Total Pages : 96 pages
Book Rating : 4.8/5 (982 download)

DOWNLOAD NOW!

Book Synopsis Ideals of Identities of Associative Algebras by : Aleksandr Robertovich Kemer

Download or read book Ideals of Identities of Associative Algebras written by Aleksandr Robertovich Kemer and published by American Mathematical Soc.. This book was released on with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the study of the structure of identities of PI-algebras over a field of characteristic zero. In the first chapter, the author brings out the connection between varieties of algebras and finitely-generated superalgebras. The second chapter examines graded identities of finitely-generated PI-superalgebras. One of the results proved concerns the decomposition of T-ideals, which is very useful for the study of specific varieties. In the fifth section of Chapter Two, the author solves Specht's problem, which asks whether every associative algebra over a field of characteristic zero has a finite basis of identities. The book closes with an application of methods and results established earlier: the author finds asymptotic bases of identities of algebras with unity satisfying all of the identities of the full algebra of matrices of order two.

Non-Associative Algebras and Related Topics

Author : Helena Albuquerque
Publisher : Springer Nature
ISBN 13 : 3031327071
Total Pages : 305 pages
Book Rating : 4.0/5 (313 download)

DOWNLOAD NOW!

Book Synopsis Non-Associative Algebras and Related Topics by : Helena Albuquerque

Download or read book Non-Associative Algebras and Related Topics written by Helena Albuquerque and published by Springer Nature. This book was released on 2023-07-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory. One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.

Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises

Download Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises PDF Online Free

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
ISBN 13 : 3960677219
Total Pages : 257 pages
Book Rating : 4.9/5 (66 download)

DOWNLOAD NOW!

Book Synopsis Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises by : Sven Bodo Wirsing

Download or read book Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2018-12-12 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the context of the Wedderburn-Malcev theorem a radical complement exists and all complements are conjugated. The main topics of this work are to analyze the Determination of a (all) radical complements, the representation of an element as the sum of a nilpotent and fully separable element and the compatibility of the Wedderburn-Malcev theorem with derived structures. Answers are presented in details for commutative and solvable associative algebras. Within the analysis the set of fully-separable elements and the generalized Jordan decomposition are of special interest. We provide examples based on generalized quaternion algebras, group algebras and algebras of traingular matrices over a field. The results (and also the theorem of Wedderburn-Malcev and Taft) are transferred to non-unitary algebras by using the star-composition and the adjunction of an unit. Within the App endix we present proofs for the Wedderburn-Malcev theorem for unitary algebras, for Taft's theorem on G-invariant radical complements for unitary algebras and for a theorem of Bauer concerning solvable unit groups of associative algebras.

Maximal nilpotent subalgebras I: Nilradicals and Cartan subalgebras in associative algebras. With 428 exercises

Author : Sven Bodo Wirsing
Publisher : diplom.de
ISBN 13 : 3960676034
Total Pages : 241 pages
Book Rating : 4.9/5 (66 download)

DOWNLOAD NOW!

Book Synopsis Maximal nilpotent subalgebras I: Nilradicals and Cartan subalgebras in associative algebras. With 428 exercises by : Sven Bodo Wirsing

Download or read book Maximal nilpotent subalgebras I: Nilradicals and Cartan subalgebras in associative algebras. With 428 exercises written by Sven Bodo Wirsing and published by diplom.de. This book was released on 2016-12-08 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the author’s doctorate time at the Christian-Albrechts-Universitat to Kiel, Salvatore Siciliano gave a stimulating talk in the upper seminar algebra theory about Cartan subalgebras in Lie algebra associates to associative algebra. This talk was the incentive for the author to analyze maximal nilpotent substructures of the Lie algebra associated to associative algebras. In the present work Siciliano's theory about Cartan subalgebras is worked off and expanded to different special associative algebra classes. In addition, a second maximal nilpotent substructure is analyzed: the nilradical. Within this analysis the main focus is to describe these substructure with the associative structure of the underlying algebra. This is successfully realized in this work. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.

Collected Mathematical Papers: Associative algebras and Riemann matrices

Author : Abraham Adrian Albert
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870556
Total Pages : 824 pages
Book Rating : 4.8/5 (75 download)

DOWNLOAD NOW!

Book Synopsis Collected Mathematical Papers: Associative algebras and Riemann matrices by : Abraham Adrian Albert

Download or read book Collected Mathematical Papers: Associative algebras and Riemann matrices written by Abraham Adrian Albert and published by American Mathematical Soc.. This book was released on with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the collected works of A. Adrian Albert, a leading algebraist of the twentieth century. Albert made many important contributions to the theory of the Brauer group and central simple algeras, Riemann matrices, nonassociative algebras and other topics. Part 1 focuses on associative algebras and Riemann matrices part 2 on nonassociative algebras and miscellany. Because much of Albert's work remains of vital interest in contemporary research, this volume will interst mathematicians in a variety of areas.

Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
ISBN 13 : 3960671962
Total Pages : 197 pages
Book Rating : 4.9/5 (66 download)

DOWNLOAD NOW!

Book Synopsis Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises by : Sven Bodo Wirsing

Download or read book Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2017-11-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra. We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras. The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du. By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups. All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.

Rings and Things and a Fine Array of Twentieth Century Associative Algebra

Author : Carl Clifton Faith
Publisher : American Mathematical Soc.
ISBN 13 : 0821836722
Total Pages : 513 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Rings and Things and a Fine Array of Twentieth Century Associative Algebra by : Carl Clifton Faith

Download or read book Rings and Things and a Fine Array of Twentieth Century Associative Algebra written by Carl Clifton Faith and published by American Mathematical Soc.. This book was released on 2004 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional algebras Goldie, and others. A special feature of the book is the in-depth study of rings with chain condition on annihilator ideals pioneered by Noether, Artin, and Jacobson and refined and extended by many later mathematicians. Two of the author's prior works, Algebra: Rings, Modules and Categories, I and II (Springer-Verlag, 1973), are devoted to the development of modern associative algebra and ring and module theory. Those bibliography of over 1,600 references and is exhaustively indexed. In addition to the mathematical survey, the author gives candid and descriptive impressions of the last half of the twentieth century in ''Part II: Snapshots of fellow graduate students at the University of Kentucky and at Purdue, Faith discusses his Fulbright-Nato Postdoctoral at Heidelberg and at the Institute for Advanced Study (IAS) at Princeton, his year as a visiting scholar at Berkeley, and the many acquaintances he met there and in subsequent travels in India, Europe, and most recently, Barcelona. Comments on the first edition: ''Researchers in algebra should find it both full references as to the origin and development of the theorem ... I know of no other work in print which does this as thoroughly and as broadly.'' --John O'Neill, University of Detroit at Mercy '' 'Part II: Snapshots of Mathematicians of my age and younger will relish reading 'Snapshots'.'' --James A. Huckaba, University of Missouri-Columbia