I need to rapidly get up to speed on the following topics, for the purposes of an internship:
- Global and local fields.
- Number fields, function fields, etc.
- Ring of integers, field of fractions.
- The property of a ring $R$ that "for any non-zero ideal $I$ of $R$, $R/I$ is finite".
These are some of the keywords and topics that my professor brought up in a short crash course on the topics I need to read up about this week. I borrowed Serge Lang's "Algebraic number theory" but I've found it too formal and abstract, I'm hoping for more motivational books. I also may need something slightly more elementary than Lang, since I haven't covered module theory and am a shaky on everything except the most elementary ring theory (the topics I've mostly covered in class are the isomorphism theorems, the various kinds of ideals, and the implications between euclidean, integral, principal etc).
I've found it difficult to really get started. Can anyone suggest a path I could follow in my reading, and ideally some book titles?