I am working on something which turned out to be isomorphic to the $\mathbb Z$-module $\mathbb Z^n$ and want to efficiently learn about its properties without needing to deal too much with more general modules or rings. I am therefore looking for a concise book, book chapter, review paper or similar on the $\mathbb Z^n$ and its module structure and features such as bases, linear maps etc.
I realise that this might be an utopistic wish, so I also welcome something that has a broader scope, e.g., $\mathbb R^n$ with $\mathbb R$ being a ring sharing many properties with $\mathbb Z$.
My prerequisites are:
- I consider myself to be knowledgable on linear algebra including more abstract topics.
- I have little knowledge of groups, rings, etc.
- English and German are fine as a language.