Galois Correspondence

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Related lectures (40)

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Pushouts in Group Theory: Universal Properties Explained

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

Geometric Sequences: Recurrence System

Covers geometric sequences and recurrence systems to find sequence terms and patterns.

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Galois Theory: Extensions and Residual Fields Log in to Mediaspace to watch this video

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

Galois Theory: The Galois Correspondence Log in to Mediaspace to watch this video

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

Decomposition & Inertia: Group Actions and Galois Theory Log in to Mediaspace to watch this video

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

Galois Theory Fundamentals Log in to Mediaspace to watch this video

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Ramification and Structure of Finite Extensions Log in to Mediaspace to watch this video

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

Galois Theory of Qp Log in to Mediaspace to watch this video

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

Finite Degree Extensions Log in to Mediaspace to watch this video

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

Galois Theory: Solvability and Radical Extensions Log in to Mediaspace to watch this video

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Galois Theory: Recap and Transitivity Log in to Mediaspace to watch this video

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

Dimension Theory of Rings Log in to Mediaspace to watch this video

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

Norm Extension in Finite Fields Log in to Mediaspace to watch this video

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

Algebras and Field Extensions Log in to Mediaspace to watch this video

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

Galois Theory: Dedekind Rings Log in to Mediaspace to watch this video

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

Hensel's Lemma and Field Theory Log in to Mediaspace to watch this video

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

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