Concept

Normal extension

Related lectures (22)

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

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

Decomposition & Inertia: Group Actions and Galois Theory

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

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Galois Theory: Extensions and Residual Fields

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

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Finite Extensions of Qp: Local Constancy

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

Algebras and Field Extensions

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

Galois Correspondence

Covers the Galois correspondence, relating subgroups to intermediate fields.

Matrix Calculations: Basis Change and Extensions

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Norm Extension in Finite Fields

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

Ramification Theory: Dedekind Recipe

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Galois Theory Fundamentals

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 Theory: Residual Fields and Discriminant Ideal

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

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Long Exact Sequence of Ext-Modules

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

Fluids and Electromagnetism

Explores Poiseuille flow, Navier-Stokes equation neglect, wave characteristics, and complex notation in fluid dynamics and wave phenomena.

Equilibrium Extension Analysis

Discusses equilibrium, extension analysis, stress distribution, and strain components' compatibility for a valid solution.

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.