Galois Theory: Recap and Transitivity

Related lectures (31)

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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.

Covers the Galois correspondence, relating subgroups to intermediate fields.

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

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

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

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

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