Algebraic Extensions

Related lectures (32)

Page 3 of 4

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

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

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

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

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

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Covers the approximation of functions in Sobolev spaces using smooth functions.

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

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.