2025-09-23

This following is a very brief summary of what happened in class on 2025-09-23.

We first noted that, with our definition of module morphism, we can now talk about the category R-Mod of left R-modules. (We briefly outlined how our definitions of modules and module morphisms did indeed define a category.)

We briefly looked at some examples of module morphisms (especially the "zero morphism" uniquely defined between any pair of R-modules), defined the notion of submodule, and then explored a connection between module morphisms and submodules, namely the kernel and image of a module morphism. (Soon we'll see how every submodule can be viewed as a kernel of a module morphism, and as an image of another module morphism, so technically these two examples cover every possible submodule.)

Concepts


Module morphisms
Submodules
Module morphisms and submodules

References