目錄
PART ONE Noncommutative Algebra
CHAPTER 1 Definitions and Examples of Groups
CHAPTER 2 Subgroups and Cosets
CHAPTER 3 Homomorphisms
CHAPTER 4 Group Actions
CHAPTER 5 The Sylow Theorems and p-groups
CHAPTER 6 Permutation Groups
CHAPTER 7 New Groups from Old
CHAPTER 8 Solvable and Nilpotent Groups
CHAPTER 9 Transfer
CHAPTER 10 Operator Groups and Unique Decompositions
CHAPTER 11 Module Theory without Rings
CHAPTER 12 Rings, Ideals, and Modules
CHAPTER 13 Simple Modules and Primitive Rings
CHAPTER 14 Artinian Rings and Projective Modules
CHAPTER 15 An Introduction to Character Theory
PART Two Commutative Algebra
CHAPTER 16 Polynomial Rings, PIDs, and UFDs
CHAPTER 17 Field Extensions
CHAPTER 18 Galois Theory
CHAPTER 19 Separability and Inseparability
CHAPTER 20 Cyclotomy and Geometric Constructions
CHAPTER 21 Finite Fields
CHAPTER 22 Roots, Radicals, and Real Numbers
CHAPTER 23 Norms, Traces, and Discriminants
CHAPTER 24 Transcendental Extensions
CHAPTER 25 The Artin-Schreier Theorem
CHAPTER 26 Ideal Theory
CHAPTER 27 Noetherian Rings
CHAPTER 28 Integrality
CHAPTER 29 Dedekind Domains
CHAPTER 30 Algebraic Sets and the Nullstellensatz
Index
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