目錄
Pt. 1 Noncommutative Algebra 1
Ch. 1 Definitions and Examples of Groups 3
Ch. 2 Subgroups and Cosets 14
Ch. 3 Homomorphisms 30
Ch. 4 Group Actions 42
Ch. 5 The Sylow Theorems and p-groups 55
Ch. 6 Permutation Groups 70
Ch. 7 New Groups from Old 83
Ch. 8 Solvable and Nilpotent Groups 99
Ch. 9 Transfer 115
Ch. 10 Operator Groups and Unique Decompositions 129
Ch. 11 Module Theory without Rings 142
Ch. 12 Rings, Ideals, and Modules 159
Ch. 13 Simple Modules and Primitive Rings 177
Ch. 14 Artinian Rings and Projective Modules 194
Ch. 15 An Introduction to Character Theory 213
Pt. 2 Commutative Algebra 231
Ch. 16 Polynomial Rings, PIDs, and UFDs 233
Ch. 17 Field Extensions 254
Ch. 18 Galois Theory 274
Ch. 19 Separability and Inseparability 293
Ch. 20 Cyclotomy and Geometric Constructions 307
Ch. 21 Finite Fields 326
Ch. 22 Roots, Radicals, and Real Numbers 342
Ch. 23 Norms, Traces, and Discriminants 359
Ch. 24 Transcendental Extensions 379
Ch. 25 The Artin-Schreier Theorem 401
Ch. 26 Ideal Theory 418
Ch. 27 Noetherian Rings 433
Ch. 28 Integrality 453
Ch. 29 Dedekind Domains 474
Ch. 30 Algebraic Sets and the Nullstellensatz 493
Index 507
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