Integral Domains: Factorisation and Noetherian Rings

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

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

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

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

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

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

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

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