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Book PI Algebras

    Book Details:
  • Author : N. Jacobson
  • Publisher : Springer
  • Release : 2006-11-15
  • ISBN : 3540374272
  • Pages : 120 pages

Download or read book PI Algebras written by N. Jacobson and published by Springer. This book was released on 2006-11-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Introduction to Applied Linear Algebra

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Book Pi   Algebras  An Introduction

Download or read book Pi Algebras An Introduction written by Nathan Jacobson and published by . This book was released on 1975 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Basic Algebra I

    Book Details:
  • Author : Nathan Jacobson
  • Publisher : Courier Corporation
  • Release : 2012-12-11
  • ISBN : 0486135225
  • Pages : 530 pages

Download or read book Basic Algebra I written by Nathan Jacobson and published by Courier Corporation. This book was released on 2012-12-11 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.

Book Introduction to Noncommutative Algebra

Download or read book Introduction to Noncommutative Algebra written by Matej Brešar and published by Springer. This book was released on 2014-10-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

Book Rings with Polynomial Identities

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 Introduction to Boolean Algebras

Download or read book Introduction to Boolean Algebras written by Steven Givant and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.

Book Introduction to Representation Theory

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 Introduction to Lie Algebras

Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Book Introduction to Lie Algebras and Representation Theory

Download or read book Introduction to Lie Algebras and Representation Theory written by J.E. Humphreys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

Book Graduate Algebra

    Book Details:
  • Author : Louis Halle Rowen
  • Publisher : American Mathematical Soc.
  • Release : 2006
  • ISBN : 9780821883976
  • Pages : 464 pages

Download or read book Graduate Algebra written by Louis Halle Rowen and published by American Mathematical Soc.. This book was released on 2006 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties. Major topics include the theory of modules over a principal ideal domain, and its applicationsto matrix theory (including the Jordan decomposition), the Galois theory of field extensions, transcendence degree, the prime spectrum of an algebra, localization, and the classical theory of Noetherian and Artinian rings. Later chapters include some algebraic theory of elliptic curves (featuring theMordell-Weil theorem) and valuation theory, including local fields. One feature of the book is an extension of the text through a series of appendices. This permits the inclusion of more advanced material, such as transcendental field extensions, the discriminant and resultant, the theory of Dedekind domains, and basic theorems of rings of algebraic integers. An extended appendix on derivations includes the Jacobian conjecture and Makar-Limanov's theory of locally nilpotent derivations. Grobnerbases can be found in another appendix. Exercises provide a further extension of the text. The book can be used both as a textbook and as a reference source.

Book Introduction To Commutative Algebra

Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Book An Introduction to Operator Algebras

Download or read book An Introduction to Operator Algebras written by Kehe Zhu and published by CRC Press. This book was released on 2018-05-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

Book Free Algebras and PI algebras

Download or read book Free Algebras and PI algebras written by Vesselin S. Drensky and published by . This book was released on 2000 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the combinatorial theory of polynomial algebras, free associative and free Lie algebras, and algebras with polynomial identities. It also examines the structure of automorphism groups of free and relatively free algebras. It is based on graduate courses and short cycles of lectures presented by the author at several universities and its goal is to involve the reader as soon as possible in the research area, to make him or her able to read books and papers on the considered topics. It contains both classical and contemporary results and methods. A specific feature of the book is that it includes as its inseparable part more than 250 exercises and examples with detailed hints (50 % of the numbered statements), some of them treating serious mathematical results. The exposition is accessible for graduate and advanced undergraduate students with standard background on linear algebra and some elements of ring theory and group theory. The professional mathematician working in the field of algebra and other related topics also will find the book useful for his or her research and teaching. TOC:Introduction 1. Commutative, Associative and Lie Algebras: Basic properties of algebras; Free algebras; The Poincaré-Birkhoff-Witt theorem. 2. Algebras with Polynomial Identities: Definitions and examples of PI-Algebras; Varieties and relatively free algebras; The theorem of Birkhoff. 3. The Specht Problem: The finite basis property; Lie algebras in characteristic 2. 4. Numerical Invariants of T-Ideals: Graded vector spaces; Homogeneous and multilinear polynomial identities; Proper polynomial identities. 5. Polynomial Identities of Concrete Algebras: Polynomial identities of the Grassmann algebra; Polynomial identities of the upper triangular matrices. 6. Methods of Commutative Algebra: Rational Hilbert series; Nonmatrix polynomial identities; Commutative and noncommutative invariant theory. 7. Polynomial Identities of the Matrix Algebras: The Amitsur-Levitzki theorem; Generic matrices; Central polynomials; Various identities of matrices. 8. Multilinear Polynomial Identities: The codimension theorem of Regev; Algebras with polynomial growth of codimensions; The Nagata-Higman theorem; The theory of Kemer. 9. Finitely Generated PI-Algebras: The problems of Burnside and Kurosch; The Shirshov theorem; Growth of algebras and Gelfand-Kirillov dimension; Gelfand-Kirillov dimension of PI-Algebras. 10. Automorphisms of Free Algebras: Automorphisms of groups and algebras; The polynomial algebra in two variables; The free associative algebra of rank two; Exponential automorphisms; Automorphisms of relatively free algebras. 11. Free Lie Algebras and Their Automorphisms: Bases and subalgebras of free Lie algebras; Automorphisms of free Lie algebras; Automorphisms of relatively free Lie algebras. 12. The Method of Representation Theory: Representations of finite groups; The symmetric group; Multilinear polynomial identities; The action of the general linear group; Proper polynomial identities; Polynomial identities of matrices.

Book Introduction to Operator Algebras

Download or read book Introduction to Operator Algebras written by Bing-Ren Li and published by World Scientific. This book was released on 1992 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.

Book Topics in Algebra

    Book Details:
  • Author : M.F. Newman
  • Publisher : Springer
  • Release : 2007-01-05
  • ISBN : 3540355499
  • Pages : 243 pages

Download or read book Topics in Algebra written by M.F. Newman and published by Springer. This book was released on 2007-01-05 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: