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A History of Abstract Algebra

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Table of Contents

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    Book Overview
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    Chapter 1 Simple Quadratic Forms
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    Chapter 2 Fermat’s Last Theorem
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    Chapter 3 Lagrange’s Theory of Quadratic Forms
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    Chapter 4 Gauss’s Disquisitiones Arithmeticae
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    Chapter 5 Cyclotomy
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    Chapter 6 Two of Gauss’s Proofs of Quadratic Reciprocity
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    Chapter 7 Dirichlet’s Lectures on Quadratic Forms
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    Chapter 8 Is the Quintic Unsolvable?
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    Chapter 9 The Unsolvability of the Quintic
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    Chapter 10 Galois’s Theory
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    Chapter 11 After Galois
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    Chapter 12 Revision and First Assignment
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    Chapter 13 Jordan’s Traité
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    Chapter 14 The Galois Theory of Hermite, Jordan and Klein
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    Chapter 15 What Is ‘Galois Theory’?
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    Chapter 16 Algebraic Number Theory: Cyclotomy
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    Chapter 17 Dedekind’s First Theory of Ideals
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    Chapter 18 Dedekind’s Later Theory of Ideals
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    Chapter 19 Quadratic Forms and Ideals
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    Chapter 20 Kronecker’s Algebraic Number Theory
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    Chapter 21 Revision and Second Assignment
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    Chapter 22 Algebra at the End of the Nineteenth Century
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    Chapter 23 The Concept of an Abstract Field
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    Chapter 24 Ideal Theory and Algebraic Curves
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    Chapter 25 Invariant Theory and Polynomial Rings
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    Chapter 26 Hilbert’s Zahlbericht
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    Chapter 27 The Rise of Modern Algebra: Group Theory
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    Chapter 28 Emmy Noether
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    Chapter 29 From Weber to van der Waerden
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    Chapter 30 Revision and Final Assignment
Attention for Chapter 25: Invariant Theory and Polynomial Rings
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Chapter title
Invariant Theory and Polynomial Rings
Chapter number 25
Book title
A History of Abstract Algebra
Published by
Springer, Cham, August 2018
DOI 10.1007/978-3-319-94773-0_25
Book ISBNs
978-3-31-994772-3, 978-3-31-994773-0
Authors

Jeremy Gray