Lectures related to Frobenius Theorems in Number Theory

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

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

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

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

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

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

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

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

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

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

Covers the embeddings of number fields and ideal classes with proofs and examples.

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

Explores prime numbers, coprime integers, and their properties in number theory.

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.