STRONGLY PRIME GROUP RINGS

Abstract

Abstract A ring R is (right) strongly prime (SP) if every nonzero two sided ideal contains a finite set whose right annihilator is zero, SP rings have been studied by Handelman and Lawrence who raised the problem of characterizing SP group algebras. They showed that if R is SP and G is torsion free Abelian, then the group ring RG is SP. The aim of this note is to determine some more group rings which are SP. For a ring R we also define the strongly prime radical s(R). We then show that s(R)G = s(W) for certain classes of groups.