Introduction to Abstract Algebra, 4/e (Hardcover) (抽象代數導論 (第4版))

<內容簡介>

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.
<章節目錄>

0 Preliminaries
1 Integers and Permutations
2 Groups
3 Rings
4 Polynomials
5 Factorization in Integral Domains
6 Fields
7 Modules over Principal Ideal Domains
8 p-Groups and the Sylow Theorems
9 Series of Subgroups
10 Galois Theory
11 Finiteness Conditions for Rings and Modules