Book:Emil Artin/Galois Theory
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Emil Artin and Arthur N. Milgram: Galois Theory
Published $\text {1942}$ (translated by Arthur N. Milgram)
Subject Matter
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.N. Milgram)
- 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
Further Editions
- 1944: Emil Artin and Arthur N. Milgram: Galois Theory (2nd ed.)