2025-09-22

This following is a very brief summary of what happened in class on 2025-09-22.

We introduced the notion of a module, which is an algebraic structure that generalizes the structures of vector spaces and abelian groups. We looked at some examples, including how each ring R can be given the structure of a left module over itself. We ended by introducing the notion of a morphism between modules. We noted that there are only morphisms between modules "of the same type", i.e., between left R-modules or right R-modules.

Next class we'll look at a bunch of examples of module morphisms, as well as the related notion of submodule.

Concepts

References