Module Theory: Noetherian Modules

This lecture covers the concept of Noetherian modules, where a module is said to be Noetherian if all its submodules are finitely generated. The instructor explains the Jordan-Hölder theorem and the notion of simple modules, illustrating that a simple module is simple if it has no nontrivial proper submodules. The lecture also delves into the composition series of a module, defining it as a chain of submodules with simple quotients. The instructor demonstrates the application of these concepts through examples and discusses the properties of Noetherian modules and their composition series.