Module Theory: Definitions and Examples

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

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

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

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

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