A First Course in Abstract Algebra, 8th Edition retains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra – and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose. This revision also includes applied topics such as RSA encryption and coding theory, as well as examples of applying Gröbner bases.
Key to the 8th Edition has been transforming from a print-based learning tool to a digital learning tool. The eText is packed with content and tools, such as mini-lecture videos and interactive figures, that bring course content to life for students in new ways and enhance instruction. A low-cost, loose-leaf version of the text is also available for purchase within the Pearson eText.
Author(s): John B. Fraleigh, Neal E. Brand
Edition: 8
Publisher: Pearson
Year: 2021
Language: English
Pages: 424+xvi
City: Hoboken, NJ
Tags: Abstract Algebra; Groups; Subgroups; Homomorphisms; Group Theory; Ring; Fields; Galois Theory
Front Cover
Title Page
Copyright Page
Contents
Instructor’s Preface
Dependence Chart
Student’s Preface
0 Sets and Relations
I Groups and Subgroups
1 Binary Operations
2 Groups
3 Abelian Examples
4 Nonabelian Examples
5 Subgroups
6 Cyclic Groups
7 Generating Sets and Cayley Digraphs
II Structure of Groups
8 Groups of Permutations
9 Finitely Generated Abelian Groups
10 Cosets and the Theorem of Lagrange
11 Plane Isometries
III Homomorphisms and Factor Groups
12 Factor Groups
13 Factor-Group Computations and Simple Groups
14 Group Action on a Set
15 Applications of G-Sets to Counting
IV Advanced Group Theory
16 Isomorphism Theorems
17 Sylow Theorems
18 Series of Groups
19 Free Abelian Groups
20 Free Groups
21 Group Presentations
V Rings and Fields
22 Rings and Fields
23 Integral Domains
24 Fermat’s and Euler’s Theorems
25 Encryption
VI Constructing Rings and Fields
26 the Field of Quotients of an Integral Domain
27 Rings of Polynomials
28 Factorization of Polynomials over a Field
29 Algebraic Coding Theory
30 Homomorphisms and Factor Rings
31 Prime and Maximal Ideals
32 Noncommutative Examples
VII Commutative Algebra
33 Vector Spaces
34 Unique Factorization Domains
35 Euclidean Domains
36 Number Theory
37 Algebraic Geometry
38 Gröbner Bases for Ideals
VIII Extension Fields
39 Introduction to Extension Fields
40 Algebraic Extensions
41 Geometric Constructions
42 Finite Fields
IX Galois Theory
43 Introduction to Galois Theory
44 Splitting Fields
45 Separable Extensions
46 Galois Theory
47 Illustrations of Galois Theory
48 Cyclotomic Extensions
49 Insolvability of the Quintic
Appendix: Matrix Algebra
Bibliography
Notations
Answers to Odd-numbered Exercises Not Asking for Definitions or Proofs
Index
