# Module theory for chapters 1-3 of Hatcher Algebraic Topology

I'm taking a graduate sequence alg. topology course based on Hatcher and I've already learned point-set topology, groups, and rings. I scanned the first three chapters of Hatcher and saw modules appearing multiple times.

I'm planning on covering enough module theory over the break from Dummit and Foote so that I can comfortably take this course without struggling to make up for my knowledge deficit:

How much of this appears in Hatcher (chap 1-3)? In the interest that I want to do well in this course, should I read chapters 11 and 12 or can I just skip them for now?

• It depends what parts you are reading. Definitely $10.1-10.4$, $11.1-11.13$, and $12.1$. If you are applying to grad school, these are basically all things you will need to learn at some point – Elliot G Dec 9 '19 at 8:10
• oh I definitely agree. I plan on learning these things, but since the course is next semester I want to know what parts are course-specific. – kyary Dec 9 '19 at 8:19

Chapter 12 might be the least important of the 12, because the PID's that appear in practice in early algebraic topology are essentially $$\mathbb Z$$ and fields (and sometimes some localisations of $$\mathbb Z$$, but the theory for them follows from that for $$\mathbb Z$$, so the general theory is not needed specifically); so you can skip chapter 12 if you know or can learn someplace else (some of) the theory of finitely generated modules over $$\mathbb Z$$ and the basic properties of free modules over $$\mathbb Z$$ (otherwise known as abelian groups)