Dedekind Rings: Theory and Applications

Related lectures (32)

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

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

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

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.