Lectures related to Module (mathematics)

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

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

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

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

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explains submodules, generated modules, and ring ideals in module structure.

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

Introduces the definition and examples of A-modules, including sub-modules and ideals.

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

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

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

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

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

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

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

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

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

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