Rings and Modules: Color Codes and Homological Algebra

Related lectures (32)

Page 1 of 4

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

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

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

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

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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

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

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

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

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