Galois Theory

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Author(s): C. Birkar, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part II Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; algebra; modern algebra; abstract algebra; polynomials

Introduction
Solving equations
Field extensions
Field extensions
Ruler and compass constructions
K-homomorphisms and the Galois Group
Splitting fields
Algebraic closures
Separable extensions
Normal extensions
The fundamental theorem of Galois theory
Finite fields
Solutions to polynomial equations
Cyclotomic extensions
Kummer extensions
Radical extensions
Solubility of groups, extensions and polynomials
Insolubility of general equations of degree 5 or more
Computational techniques
Reduction mod p
Trace, norm and discriminant