Understanding Modulus Arithmetic

Question

I'm looking for a short text or primer (maybe max 20-30 pages) which explains the basics of modulus arithmetic and how it apply to rings. Specifically, I'm looking for a text that explains how the maps $\mathbb{Z}/p^{n+1}\mathbb{Z} \to \mathbb{Z}/p^{n}\mathbb{Z}$, $\mathbb{Z}/p^{m}\mathbb{Z} \to \mathbb{Z}/p^{n}\mathbb{Z}$,and $\mathbb{Z}/p^{m-n}\mathbb{Z} \to p^{n}\mathbb{Z}/p^{m}\mathbb{Z}$ $(m \ge n$) "work". I'm just very shaky when working in modulus arithmetic...

Answer 1

As I recall Joseph Silverman's A Friendly Introduction to Number Theory has a pretty good chapter on modular arithmetic...

Also you could look up the relevant sections in Fraleigh's A First Course in Abstract Algebra... for more on the rings (and mappings, i suspect) you mentioned...

Modular arithmetic is fundamental in both subjects, and while I don't know of any short primer, the chapter in Silverman should be around $10-20$ pages, for instance...

I highly recommend both books...