Galois Theory: Extensions and Residual Fields

Related lectures (32)

Page 2 of 4

Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.

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

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

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

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.