PART TWO Commutative Algebra 231 CHAPTE R 16 Polynomial Rings, PIDs, and UFDs 233 CHAPTE R 17 Field Extensions 254 CHAPTE R 18 Galois Theory 274 CHAPTE R 19 Separability and Inseparability 293 CHAPTE R 20 Cyclotomy and Geometric Constructions 307 CHAPTE R 21 Finite Fields 326 CHAPTE R 22 Roots, Radicals, and Real Numbers 342 CHAPTE R 23 Norms, Traces, and Discriminants 359 CHAPTE R 24 Transcendental Extensions 379

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