Lectures related to Dimension theory of rings

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.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

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

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

Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.

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

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

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