Dimension theory of rings

Related lectures (32)

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

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.

Covers induced homomorphisms on relative homology groups and their properties.

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

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Discusses irreducible factors in rings and the properties of Noetherian rings.

Covers the basics of finite fields, including arithmetic operations and properties.

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