Lectures related to Rings and Modules: Integral Extensions

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

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

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

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Explores Python modules, program hierarchy, module importing, and namespaces, including variables and scopes within functions.

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Covers free resolution of modules and projective modules in module theory.