Associative Algebras

Author : R.S. Pierce
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781475701630

Get Book

Associative Algebras by R.S. Pierce Pdf

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.

Author : Mercedes Siles Molina,Laiachi El Kaoutit,Mohamed Louzari,L'Moufadal Ben Yakoub,Mohamed Benslimane
Publisher : Springer Nature
Page : 338 pages
File Size : 48,9 Mb
Release : 2020-01-02
Category : Mathematics
ISBN : 9783030352561

Get Book

Associative and Non-Associative Algebras and Applications by Mercedes Siles Molina,Laiachi El Kaoutit,Mohamed Louzari,L'Moufadal Ben Yakoub,Mohamed Benslimane Pdf

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.

Author : Charles W. Curtis,Irving Reiner
Publisher : American Mathematical Soc.
Page : 722 pages
File Size : 50,7 Mb
Release : 1966
Category : Mathematics
ISBN : 0821869450

Get Book

Representation Theory of Finite Groups and Associative Algebras by Charles W. Curtis,Irving Reiner Pdf

Author : Aleksandr Robertovich Kemer
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 47,5 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 0821898299

Get Book

Ideals of Identities of Associative Algebras by Aleksandr Robertovich Kemer Pdf

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.

Author : Ibrahim Assem,Daniel Simson,Andrzej Skowronski
Publisher : Cambridge University Press
Page : 480 pages
File Size : 55,7 Mb
Release : 2006-02-13
Category : Mathematics
ISBN : 052158423X

Get Book

Elements of the Representation Theory of Associative Algebras: Volume 1 by Ibrahim Assem,Daniel Simson,Andrzej Skowronski Pdf

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.

Author : Alexander Abian
Publisher : Elsevier
Page : 175 pages
File Size : 41,5 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483186795

Get Book

Linear Associative Algebras by Alexander Abian Pdf

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.

Author : Charles W. Curtis,Irving Reiner
Publisher : American Mathematical Soc.
Page : 714 pages
File Size : 50,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821840665

Get Book

Representation Theory of Finite Groups and Associative Algebras by Charles W. Curtis,Irving Reiner Pdf

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.

Author : Susumu Okubo
Publisher : Cambridge University Press
Page : 152 pages
File Size : 42,8 Mb
Release : 1995-08-03
Category : Mathematics
ISBN : 9780521472159

Get Book

Introduction to Octonion and Other Non-Associative Algebras in Physics by Susumu Okubo Pdf

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.

Author : Abraham Adrian Albert,Richard E. Block
Publisher : American Mathematical Soc.
Page : 824 pages
File Size : 50,7 Mb
Release : 2024-07-03
Category : Associative algebras
ISBN : 0821870556

Get Book

Collected Mathematical Papers: Associative algebras and Riemann matrices by Abraham Adrian Albert,Richard E. Block Pdf

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.

Author : Robin Hirsch,Ian Hodkinson
Publisher : Gulf Professional Publishing
Page : 722 pages
File Size : 51,9 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0444509321

Get Book

Relation Algebras by Games by Robin Hirsch,Ian Hodkinson Pdf

In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. P The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given.-

Author : Shavkat Ayupov,Bakhrom Omirov,Isamiddin Rakhimov
Publisher : CRC Press
Page : 157 pages
File Size : 40,6 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781000740400

Get Book

Leibniz Algebras by Shavkat Ayupov,Bakhrom Omirov,Isamiddin Rakhimov Pdf

Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts

Author : Carl Clifton Faith
Publisher : American Mathematical Soc.
Page : 513 pages
File Size : 50,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836729

Get Book

Rings and Things and a Fine Array of Twentieth Century Associative Algebra by Carl Clifton Faith Pdf

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

Author : Freddy Van Oystaeyen
Publisher : CRC Press
Page : 310 pages
File Size : 42,5 Mb
Release : 2000-06-06
Category : Mathematics
ISBN : 082470424X

Get Book

Algebraic Geometry for Associative Algebras by Freddy Van Oystaeyen Pdf

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level.

Author : W.A. de Graaf
Publisher : Elsevier
Page : 407 pages
File Size : 51,7 Mb
Release : 2000-02-04
Category : Mathematics
ISBN : 9780080535456

Get Book

Lie Algebras: Theory and Algorithms by W.A. de Graaf Pdf

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Author : Richard D. Schafer
Publisher : Courier Dover Publications
Page : 176 pages
File Size : 47,5 Mb
Release : 2017-11-15
Category : Mathematics
ISBN : 9780486164175

Get Book

An Introduction to Nonassociative Algebras by Richard D. Schafer Pdf

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.