Introduction to group rings (reference request) I'm looking for a thorough introduction to group rings, specifically the simple case of group rings over the integers where the group is abelian and finitely generated. I realise that these are quotients of polynomial rings over the integers in finitely many variables, but I'm interested also in the perspective from group rings. Specifically I'd like to know, given such a group, methods to determine whether the group ring is connected, reduced and/or a domain, what its unit group is, etc.

You can read "Groups, Rings and Galois Theory" by Victor. P. Snaith. It provides a good introduction on the topic. Also, "Groups, Rings and Modules" by Auslander and Buchsbaum is quite good. Hope it helps.  
