Fields and Galois Theory

• Main Author: Howie, John M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2006.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Algebra.; Field theory (Physics).; Field Theory and Polynomials.

The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteri...

Table of Contents:

• Rings and Fields
• Integral Domains and Polynomials
• Field Extensions
• Applications to Geometry
• Splitting Fields
• Finite Fields
• The Galois Group
• Equations and Groups
• Some Group Theory
• Groups and Equations
• Regular Polygons
• Solutions.