Zero-divisors and idempotents in group rings
After a brief introduction of the basic properties of group rings, some famous theorems on traces of idempotent elements of group rings will be presented. Next we consider some famous conjectures stated by Irving Kaplansky, among them the zero-divisor conjecture. The conjecture asserts that if a group ring is constructed from a field (or an integral domain) and a torsion-free group, then it does n
