Algebra: Abstract and Modern

15

Galois Theory

15.1 Separable and Normal Extensions

15.2 Automorphism Groups and Fixed Fields

15.3 Fundamental Theorem of Galois Theory

Galois theory of fields is one of the most elegant theories in Abstract Algebra and it is an excellent combination of group theory and the theory of algebraic field extensions. In general, Galois theory and, in particular, the fundamental theorem of Galois theory has several applications to the theory of equations and geometry. Although we are not making a detailed study of Galois theory, we shall discuss its fundamental concepts and give certain simple applications like proving the fundamental theorem of algebra and the nonconstructability of certain geometric figures using straightedge and compass alone. ...