Fundamentals of Abstract Algebra / Edition 1

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This new addition to the International Series in Pure and Applied Mathematics is for the two-term advanced undergraduate course in abstract algebra. Each chapter consists of definitions, theorems, proofs, and corollaries. There are also numerous examples that help illustrate the concepts. A unique feature of this text is the worked-out exercises that appear after every section. These worked-out exercises provide techniques of problem solving for students. Sprinkled throughout the text are comments dealing with the historical development of abstract algebra as well as profiles of notable mathematicians. Special topics, such as algebraic varieties, matrix rings, and Noetherian and Artinian rings, are also included for those instructors who want additional material.
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Product Details

Table of Contents

List of Symbols
1 Sets, Relations, and Integers 1
2 Introduction to Groups 57
3 Permutation Groups 83
4 Subgroups and Normal Subgroups 99
5 Homomorphisms and Isomorphisms of Groups 140
6 Direct Product of Groups 181
7 Sylow Theorems 190
8 Solvable and Nilpotent Groups 223
9 Finitely Generated Abelian Groups 247
10 Introduction to Rings 269
11 Subrings, Ideals, and Homomorphisms 289
12 Ring Embeddings 318
13 Direct Sum of Rings 326
14 Polynomial Rings 335
15 Euclidean Domains 345
16 Unique Factorization Domains 367
17 Maximal, Prime, and Primary Ideals 389
18 Noetherian and Artinian Rings 406
19 Modules and Vector Spaces 422
20 Rings of Matrices 434
21 Field Extensions 445
22 Multiplicity of Roots 474
23 Finite Fields 492
24 Galois Theory and Applications 500
25 Geometric Constructions 538
26 Coding Theory 549
27 Grobner Bases 574
Selected Bibliography 602
Answers and Hints to Selected Exercises 605
Index 628
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