A ring is called an almost pp− ring if the annihilator of each element of
R is generated by its idempotents. We prove that for a ring R and an Abelian group
G, if the group ring RG is an almost pp− ring then so is R, Moreover, if G is a finite
Abelian group then |G|
−1
∈ R. Then we give a counter example to the converse of this.
Also, we prove that RG is an almost pp−ring if and only if RH is an almost pp− ring
for every subgroup H of G. It is proved that the polynomial ring R [x] is an almost pp−
ring if and only if R is an almost pp− ring. Finally, we prove that the power series ring
R [[x]]is an almost pp− ring if and only if for any two countable subsets S and T of R
such that S ⊆ AnnR (T), there exists an idempotent e ∈ AnnR (T) such that b = be for
all b ∈ S.
Keywords: almost pp−ring, group ring, polynomial ring, power series ring