Galois theory

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Galois theory / David A. Cox

資料種別:: 電子ブック
出版情報:: Wiley Online Library - AutoHoldings Books
Hoboken : John Wiley & Sons, Incorporated, 2012
著者名:: Cox, David A.
ISBN:: 9781118072059 [1118072057]
9786613618191 [6613618195]
書誌ID:: OB00565044

子書誌情報

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所蔵情報

書誌詳細

言語:

英語

目次情報:

Preface to the First Edition

Preface to the Second Edition

Notation

Basic Notation / 1：

Chapter-by-Chapter Notation / 2：

Polynomials / Part I：

Cubic Equations

Cardan's Formulas / 1.1：

Permutations of the Roots / 1.2：

Cubic Equations over the Real Numbers / 1.3：

Symmetric Polynomials

Polynomials of Several Variables / 2.1：

Computing with Symmetric Polynomials (Optional) / 2.2：

The Discriminant / 2.4：

Roots of Polynomials / 3：

The Existence of Roots / 3.1：

The Fundamental Theorem of Algebra / 3.2：

Fields / Part II：

Extension Fields / 4：

Elements of Extension Fields / 4.1：

Irreducible Polynomials / 4.2：

The Degree of an Extension / 4.3：

Algebraic Extensions / 4.4：

Normal and Separable Extensions / 5：

Splitting Fields / 5.1：

Normal Extensions / 5.2：

Separable Extensions / 5.3：

Theorem of the Primitive Element / 5.4：

The Galois Group / 6：

Definition of the Galois Group / 6.1：

Galois Groups of Splitting Fields / 6.2：

Examples of Galois Groups / 6.3：

Abelian Equations (Optional) / 6.5：

The Galois Correspondence / 7：

Galois Extensions / 7.1：

Normal Subgroups and Normal Extensions / 7.2：

The Fundamental Theorem of Galois Theory / 7.3：

First Applications / 7.4：

Automorphisms and Geometry (Optional) / 7.5：

Applications / Part III：

Solvability by Radicals / 8：

Solvable Groups / 8.1：

Radical and Solvable Extensions / 8.2：

Solvable Extensions and Solvable Groups / 8.3：

Simple Groups / 8.4：

Solving Polynomials by Radicals / 8.5：

The Casus Irreducbilis (Optional) / 8.6：

Cyclotomic Extensions / 9：

Cyclotomic Polynomials / 9.1：

Gauss and Roots of Unity (Optional) / 9.2：

Geometric Constructions / 10：

Constructible Numbers / 10.1：

Regular Polygons and Roots of Unity / 10.2：

Origami (Optional) / 10.3：

Finite Fields / 11：

The Structure of Finite Fields / 11.1：

Irreducible Polynomials over Finite Fields (Optional) / 11.2：

Further Topics / Part IV：

Lagrange, Galois, and Kronecker / 12：

Lagrange / 12.1：

Galois / 12.2：

Kronecker / 12.3：

Computing Galois Groups / 13：

Quartic Polynomials / 13.1：

Quintic Polynomials / 13.2：

Resolvents / 13.3：

Other Methods / 13.4：

Solvable Permutation Groups / 14：

Polynomials of Prime Degree / 14.1：

Imprimitive Polynomials of Prime-Squared Degree / 14.2：

Primitive Permutation Groups / 14.3：

Primitive Polynomials of Prime-Squared Degree / 14.4：

The Lemniscate / 15：

Division Points and Arc Length / 15.1：

The Lemniscatic Function / 15.2：

The Complex Lemniscatic Function / 15.3：

Complex Multiplication / 15.4：

Abel's Theorem / 15.5：

Abstract Algebra / A：

Basic Algebra / A.1：

Complex Numbers / A.2：

Polynomials with Rational Coefficients / A.3：

Group Actions / A.4：

More Algebra / A.5：

Index

Preface to the First Edition

Preface to the Second Edition

Notation

Basic Notation / 1：

Chapter-by-Chapter Notation / 2：

Polynomials / Part I：

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