Author(s): Marvin Marcus
Series: Pure and Applied Mathematics
Edition: 1
Publisher: Marcel Dekker
Year: 1978
Language: English
Pages: 509
City: New York NY
Tags: Abstract Algebra
Contents
Preface vii
1 . Basic Structures 1
1.1 Sets and Functions 1
Exercises 14
Glossary 15
1.2 Algebraic Structures 16
Exercises 25
Glossary 30
1.3 Permutation Groups 31
Exercises 52
Glossary 54
2. Groups 56
2.1 Isomorphism Theorems 56
Exercises 33
Glossary 86
2.2 Group Actions and the Sylow Theorems 86
Exercises 106
Glossary 109
2.3 Some Additional Topics 109
Exercises 123
Glossary 123
3. Rings and Fields 124
3.1 Basic Facts 124
Exercises 136
Glossary 138
3.2 Introduction to Polynomial Rings 139
Exercises 170
Glossary 172
3.3 Unique Factorization Domains 1'13
Exercises 190
Glossary 193
3.4 Polynomial Factorization 194
Exercises 216
Glossary 224
3.5 Polynomials and Resultants 225
Exercises 255
Glossary 257
3.6 Applications to Geometric Constructions 257
Exercises 263
Glossary 264
3.7 Galois Theory 264
Exercises 282
Glossary 235
4. Modules and Linear Operators 28?
4.1 The Hermite Normal Form 287
Exercises 316
Glossary 319
4.2 The Smith Normal Form 320
Exercises 344
Glossary 350
4.3 The Structure of Linear Transformations 351
Exercises 381
Glossary 396
4.4 Introduction to Multilinear Algebra 396
Exercises 411
Glossary 412
5. Representations of Groups 413
5.1 Representations 413
Exercises 435
Glossary 439
5.2 Matrix Representations 440
Exercises 474
Glossary 477
Index 479
