Number Fields: Embeddings and Ideal Classes

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Related lectures (31)

Canonical Embedding: Fields and Lattices

Explores canonical embedding of #-fields, lattices, and finiteness of class groups.

Chinese Remainder Theorem: Euclidean Domains

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

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Properties of Euclidean Domains

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

Integral Domains: Factorisation and Noetherian Rings

Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Dedekind Rings: Theory and Applications

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

Hermite Normal Form: Computation & Properties

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Integral Representations: Quadratic Lattices and Hasse Principle

Explores integral representations, quadratic lattices, and the Hasse Principle.

Ramification Theory: Dedekind Recipe

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

Lattice Theory: Minkowski's Theorems

Delves into lattice theory, emphasizing Minkowski's theorems and their implications on lattice structures.

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