Algebra

Table of Contents

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   Book Overview
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   Chapter 1 Constructibility with Ruler and Compass
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   Chapter 2 Algebraic Extensions
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   Chapter 3 Simple Extensions
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   Chapter 4 Fundamentals of Divisibility
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   Chapter 5 Prime Factorization in Polynomial Rings. Gauss’s Theorem
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   Chapter 6 Polynomial Splitting Fields
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   Chapter 7 Separable Extensions
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   Chapter 8 Galois Extensions
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    Chapter 9 Finite Fields, Cyclic Groups and Roots of Unity
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    Chapter 10 Group Actions
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    Chapter 11 Applications of Galois Theory to Cyclotomic Fields
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    Chapter 12 Further Steps into Galois Theory
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    Chapter 13 Norm and Trace
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    Chapter 14 Binomial Equations
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    Chapter 15 Solvability of Equations
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    Chapter 16 Integral Ring Extensions with Applications to Galois Theory
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    Chapter 17 The Transcendence of π
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    Chapter 18 Fundamentals of Transcendental Field Extensions
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    Chapter 19 Hilbert’s Nullstellensatz