Book description
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 WedderburnArtin theorem
Throughout the book, worked examples and realworld 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 upperundergraduate and beginninggraduate levels. The book also serves as a valuable reference and selfstudy tool for practitioners in the fields of engineering, computer science, and applied mathematics.
Table of contents
 Cover
 Title Page
 Copyright
 Preface
 Acknowledgments
 Notation Used in the Text
 A Sketch of the History of Algebra to 1929
 Chapter 0: Preliminaries
 Chapter 1: Integers and Permutations

Chapter 2: Groups
 2.1 Binary Operations
 2.2 Groups
 2.3 Subgroups
 2.4 Cyclic Groups and the Order of an Element
 2.5 Homomorphisms and Isomorphisms
 2.6 Cosets and Lagrange's Theorem
 2.7 Groups of Motions and Symmetries
 2.8 Normal Subgroups
 2.9 Factor Groups
 2.10 The Isomorphism Theorem
 2.11 An Application to Binary Linear Codes
 Chapter 3: Rings
 Chapter 4: Polynomials
 Chapter 5: Factorization in Integral Domains
 Chapter 6: Fields
 Chapter 7: Modules over Principal Ideal Domains
 Chapter 8: pGroups and the Sylow Theorems
 Chapter 9: Series of Subgroups
 Chapter 10: Galois Theory
 Chapter 11: Finiteness Conditions for Rings and Modules
 Appendices
 Bibliography
 Selected Answers
 Index
Product information
 Title: Introduction to Abstract Algebra, 4th Edition
 Author(s):
 Release date: March 2012
 Publisher(s): Wiley
 ISBN: 9781118135358
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