Basic Abstract Algebra

  • Filename: basic-abstract-algebra.
  • ISBN: 0521466296
  • Release Date: 1994-11-25
  • Number of pages: 487
  • Author: P. B. Bhattacharya
  • Publisher: Cambridge University Press

This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.

Basic Abstract Algebra

  • Filename: basic-abstract-algebra.
  • ISBN: 9780486318110
  • Release Date: 2013-06-17
  • Number of pages: 432
  • Author: Robert B. Ash
  • Publisher: Courier Corporation

Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.

Elements of Abstract Algebra

  • Filename: elements-of-abstract-algebra.
  • ISBN: 9780486140353
  • Release Date: 2012-07-06
  • Number of pages: 224
  • Author: Allan Clark
  • Publisher: Courier Corporation

Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

Introduction to Abstract Algebra

  • Filename: introduction-to-abstract-algebra.
  • ISBN: 9781118135358
  • Release Date: 2012-03-20
  • Number of pages: 535
  • Author: W. Keith Nicholson
  • Publisher: John Wiley & Sons

Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

A History of Abstract Algebra

  • Filename: a-history-of-abstract-algebra.
  • ISBN: 9780817646851
  • Release Date: 2007-09-20
  • Number of pages: 168
  • Author: Israel Kleiner
  • Publisher: Springer Science & Business Media

This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.

Abstract Algebra

  • Filename: abstract-algebra.
  • ISBN: 9781584886891
  • Release Date: 2007-09-25
  • Number of pages: 472
  • Author: Paul B. Garrett
  • Publisher: CRC Press

Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.

A Book of Abstract Algebra

  • Filename: a-book-of-abstract-algebra.
  • ISBN: 9780486134796
  • Release Date: 2012-05-11
  • Number of pages: 400
  • Author: Charles C Pinter
  • Publisher: Courier Corporation

Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 1990 edition.

Concrete Abstract Algebra

  • Filename: concrete-abstract-algebra.
  • ISBN: 0521534100
  • Release Date: 2003-10-16
  • Number of pages: 240
  • Author: Niels Lauritzen
  • Publisher: Cambridge University Press

This 2003 book presents abstract algebra based on concrete examples and applications. All the traditional material with exciting directions.

Abstract Algebra

  • Filename: abstract-algebra.
  • ISBN:
  • Release Date: 2004
  • Number of pages: 932
  • Author: David S. Dummit
  • Publisher: John Wiley & Sons

Covering such material as tensor products, commutative rings, algebraic number theory and introductory algebraic geometry, this work includes exercises ranging in scope from routine to fairly sophisticated, including exploration of important theoretical or computational techniques.

Abstract Algebra

  • Filename: abstract-algebra.
  • ISBN: 0486688887
  • Release Date: 1964
  • Number of pages: 624
  • Author: W. E. Deskins
  • Publisher: Courier Corporation

This excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. These systems, which consist of sets of elements, operations, and relations among the elements, and prescriptive axioms, are abstractions and generalizations of various models which evolved from efforts to explain or discuss physical phenomena. In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diophantine problems, and congruences. Chapters 6 through 9 examine groups, rings, domains, fields, polynomial rings, and quadratic domains. Chapters 10 through 13 cover modular systems, modules and vector spaces, linear transformations and matrices, and the elementary theory of matrices. The author, Professor of Mathematics at the University of Pittsburgh, includes many examples and, at the end of each chapter, a large number of problems of varying levels of difficulty.

Algebra I A Basic Course in Abstract Algebra

  • Filename: algebra-i-a-basic-course-in-abstract-algebra.
  • ISBN: 9788131797624
  • Release Date:
  • Number of pages: 780
  • Author: Rajendra Kumar Sharma
  • Publisher: Pearson Education India

Algebra is a compulsory paper offered to the undergraduate students of Mathematics. The majority of universities offer the subject as a two /three year paper or in two/three semesters. Algebra I: A Basic Course in Abstract Algebra covers the topic required for a basic course.

Abstract Algebra Manual

  • Filename: abstract-algebra-manual.
  • ISBN: 159033924X
  • Release Date: 2004-01-01
  • Number of pages: 117
  • Author: Ayman Badawi
  • Publisher: Nova Publishers

This is the most current textbook in teaching the basic concepts of abstract algebra. The author finds that there are many students who just memorise a theorem without having the ability to apply it to a given problem. Therefore, this is a hands-on manual, where many typical algebraic problems are provided for students to be able to apply the theorems and to actually practice the methods they have learned. Each chapter begins with a statement of a major result in Group and Ring Theory, followed by problems and solutions. Contents: Tools and Major Results of Groups; Problems in Group Theory; Tools and Major Results of Ring Theory; Problems in Ring Theory; Index.

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