Lecture

Rings and Modules: Integral Extensions

Related lectures (32)

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.

Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores modules, sub-modules, and morphisms in algebraic structures.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Covers sheaves and modules, including morphisms, sheafification, cocalization, and direct image properties.