Simple quotient rings of group algebras

Abstract

Suppose KG is a prime nonsingular group algebra with maximal right quotient ring Q. We show that if N is a normal subgroup of G having only countable conjugacy classes and KN has no uniform right ideals, then Q is directly infinite and I ∩ KN = 0 for any proper ideal I of Q. Using an intersection theorem due to Zalesskiǐ we deduce that when G is soluble Q is a simple ring. We develop another intersection theorem and apply it to the case where G is either a periodic linear group or a certain type of uncountable wreath product.