Algebra. A graduate course

✍ Scribed by Isaacs I.M.

• Publisher: Brooks
• Year: 1993
• Tongue: English
• Leaves: 528
• Category: Library

✦ Synopsis

Isaacs' love for algebra and his more than 25 years of teaching experience in mathematics is evident throughout the book. In order to draw students into the material, Isaacs offers numerous examples and exercises and he seldom teaches a definition unless it leads to some interesting or exciting theorem. A number of specialized topics are included, so professors may design a course that is compatible with their own tastes. Students using this book should have knowledge of the basic ideas of group theory, ring theory, and field theory. They should know elementary linear algebra and matrix theory and they should be comfortable with mathematical proofs (how to read them, invent them, and write them).

✦ Table of Contents

Preface......Page 3
Contents......Page 8
PART ONE: Noncommutative Algebra ......Page 13
CHAPTER ONE: Definitions and Examples of Groups ......Page 15
CHAPTER TWO: Subgroups and Cosets ......Page 26
CHAPTER THREE: Homomorphisms ......Page 42
CHAPTER FOUR: Group Actions ......Page 54
CHAPTER FIVE: The Sylow Theorems and p-groups......Page 67
CHAPTER SIX: Permutation Groups......Page 82
CHAPTER SEVEN: New Groupsfrom Old ......Page 95
CHAPTER EIGHT: Solvable and Nilpotent Groups ......Page 111
CHAPTER NINE:Transfer ......Page 127
CHAPTER TEN: Operator Groups and Unique Decompositions......Page 141
CHAPTER ELEVEN: Module Theory without Rings ......Page 154
CHAPTER TWELVE: Rings, Ideals, and Modules......Page 171
CHAPTER THIRTEEN: Simple Modules and Primitive Rings ......Page 189
CHAPTER FOURTEEN: Artinian Rings and Projective Modules......Page 206
CHAPTER FIFTEEN: An Introduction to Character Theory......Page 225
PART TWO: Commutative Algebra ......Page 243
CHAPTER SIXTEEN: Polynomial Rings, PIDs, and UFDs ......Page 245
CHAPTER SEVENTEEN: Field Extensions ......Page 266
CHAPTER EIGHTEEN ......Page 286
CHAPTER NINETEEN: Separability and Inseparability ......Page 305
CHAPTER TWENTY: Cyclotomy and Geometric Constructions ......Page 319
CHAPTER TWENTY-ONE: Finite Fields......Page 338
CHAPTER TWENTY-TWO: Roots, Radicals, and Real Numbers ......Page 354
CHAPTER TWENTY-THREE: Norms, Traces, and Discriminants ......Page 371
CHAPTER TWENTY-FOUR: Transcendental Extensions ......Page 391
CHAPTER TWENTY-FIVE: The Artin-Schreier Theorem ......Page 413
CHAPTER TWENTY-SIX: Ideal Theory ......Page 430
CHAPTER TWENTY-SEVEN: Noetherian Rings ......Page 445
CHAPTER TWENTY-EIGHT: Integrality ......Page 465
CHAPTER TWENTY-NINE: Dedekind Domains ......Page 486
CHAPTER THIRTY: Algebraic Sets and the Nullstellensatz ......Page 505
Index ......Page 519