Galois Theory: Solvability and Radical Extensions

Related lectures (57)

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

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

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

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Covers the process of determining coefficients in polynomial equations.

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

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

Covers the classification of comport p-adic fields using integration and Igusa's local zeta functions.

Explores polynomial equations in complex numbers, constructibility conditions, roots of unity, and Fermat primes.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Explores the Hom functor for abelian groups and its relation to direct sums.

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Page 2 of 3