Lectures related to Simple extension

Dimension Theory of Rings

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

P-adic Numbers: Completion and Norm

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

Galois Theory: Extensions and Residual Fields

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

Integration of Simple Elements

Covers the integration of simple elements and limit expansions with examples.

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Algebras and Field Extensions

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

Algebraic Decomposition: Understanding Simple Algebraic Structures

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

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.

Matrix Calculations: Basis Change and Extensions

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

Ramification Theory: Residual Fields and Discriminant Ideal

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

Finite Degree Extensions

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

Galois Correspondence

Covers the Galois correspondence, relating subgroups to intermediate fields.

Multiple Integrals: Extension and Properties

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

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.

Integration of Rational Functions

Covers the integration of rational functions, focusing on decomposing functions into simpler elements.

Norm Extension in Finite Fields

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