Principal Ideal Domains: Structure and Homomorphisms

Related lectures (32)

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

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

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

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

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

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

Covers the operations in rings, ideals, classes, and quotient rings.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

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