Module Generation: Submodules and Modulus

This lecture covers the concept of module generation, including the definition of the smallest submodule containing an element, the generation of a modulus by a subset, and the generation of a module by a collection of submodules. It also discusses the generation of a module by linear combinations, the null modulus, and the properties of generated modules. The lecture further explores the notion of a module being of finite type, the generator of a module, and the canonical basis of a module. Additionally, it delves into the concept of a family of generators, morphisms of modules, and the compatibility of modules with certain laws.