Galois Theory Fundamentals

Related lectures (32)

Page 1 of 4

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Explores the Galois correspondence and solvability by radicals in polynomial equations.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Covers the Galois correspondence, relating subgroups to intermediate fields.