Module Theory for the Working Student Question:

What level of familiarity and comfort with modules should someone looking to work through Hatcher's Algebraic Topology possess?

Motivation:
I am taking my first graduate course in Algebraic Topology this coming October. The general outline of the course is as follows:


*

*Homotopy, homotopy invariance, mapping cones, mapping cylinders

*Fibrations, cofibrations, homotopy groups, long-exact sequences

*Classifying spaces of groups

*Freudenthal, Hurewicz, and Whitehead theorems

*Eilenberg-MacLane spaces and Postnikov towers.


I have spent a good deal of this summer trying to fortify and expand the foundations of my mathematical knowledge. In particular, I have been reviewing basic point-set and algebraic topology and a bit of abstract algebra. My knowledge of module theory is a bit lacking, though. I've only covered the basics of the following topics: submodules, algebras, torsion modules, quotient modules, module homomorphisms, finitely generated modules, direct sums, free modules, and a little bit about $\text{Hom}$ and exact sequences, so I have a working familirity with these ideas. As I do not have much time left before the beginning of the semester, I am trying to make my studying as economical as possible. So perhaps a more targeted question is:

What results and topics in module theory should every student in Algebraic Topology know?    


Looks like you'll definitely want to know the homological aspects: projective, injective and flat modules. There are lots of different characterizations for these which are useful to know. (Sorry, don't know the insides of D&F very well, perhaps it is covered.)
The Fundamental theorem of finitely generated modules over a principal ideal domain is a pretty good one to know too, since it kind of bundles up the entire theory of linear algebra.
(How much algebraic geometry do you know?)
