P.P. PROPERTIES OF GROUP RINGS

Abstract

A ring is called left p.p. if the left annihilator of each element of R is generated by an idempotent. We prove that for a ring R and a group G, if the group ring RG is left p.p. then so is RH for every subgroup H of G; if in addition G is finite then |G|−1 ∈ R. Counterexamples are given to answer the question whether the group ring RG is left p.p. if R is left p.p. and G is a finite group with |G|−1 ∈ R. Let G be a group acting on R as automorphisms. Some sufficient conditions are given for the fixed ring RG to be left p.p.