Book:Emil Artin/Galois Theory

Subject Matter

 * Galois Theory

Contents

 * $\text {I}$. LINEAR ALGEBRA
 * A. Fields
 * B. Vector Spaces
 * C. Homogeneous Linear Equations
 * D. Dependence and Independence of Vectors
 * E. Non-homogeneous Linear Equations


 * $\text {II}$. Field Theory
 * A. Extension Fields
 * B. Polynomials
 * C. Algebraic Elements
 * D. Splitting Fields
 * E. Unique Decomposition of Polynomials into Irreducible Factors
 * F. Group Characters
 * G. Normal Extensions
 * H. Finite Fields
 * I. Roots of Unity
 * J. Noether's Equations
 * K. Kummer's Fields
 * L. Simple Extensions
 * M. Existence of a Normal Basis
 * N. Theorem on Natural Irrationalities


 * $\text {III}$. Applications (by )
 * A. Solvable Groups
 * B. Permutation Groups
 * C. Solution of Equations by Radicals
 * D. The General Equation of Degree $n$
 * E. Solvable Equations of Prime Degree
 * F. Ruler and Compass Construction


 * Bibliography
 * Index