Introduction to group rings (reference request)

Question

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.

Answer 1

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.

Answer 2

You may find useful these books:

• Group Ring Groups by Eric Jespers and Ángel del Río

• The Algebraic Structure of Group Rings by Donald Passman

• Topics in group rings by Sudarshan Sehgal

• An Introduction to Group Rings - Algebras & Applications by Sudarshan Sehgal and Cesar Polcino Milies