For readers with a basic graduate level background in algebra, these ten articles provide a readable introduction to three major interrelated subjects of noncommutative algebra. The theme is the interplay between group theory and ring theory, dealing specifically with group rings, crossed products, and the Galois theory of rings. The author has carefully included most definitions, to keep the required background minimal. Furthermore, each article contains a selection of results on the given topic, a limited number of proofs or sketches, and at least a few open problems.

Readership

Table of Contents

• $\Delta$-methods in group rings
• The Jacobson radical of group rings
• Zero divisors in group rings
• Polycyclic group rings
• Crossed products of finite groups
• Crossed products of infinite groups
• Computing the symmetric ring of quotients
• Galois theory and crossed products
• Galois theory of prime rings
• Rings and fixed rings