Commutative Algebra: Recollections

Related lectures (32)

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

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

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

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

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

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

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

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

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

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