Galois Correspondence

Related lectures (32)

Page 2 of 4

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

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

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

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

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

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Covers the construction and universal properties of pushouts in group theory.

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

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.