Two properties of the power series ring

For a commutative ring with unity, A , it is proved that the power series ring A 〚 X 〛 is a PF‐ring if and only if for any two countable subsets S and T of A such that , there exists such that b c = b for all b ∈ S . Also it is proved that a power series ring A 〚 X 〛 is a PP‐ring if and only if A is a PP‐ring in which every increasing chain of idempotents in A has a supremum which is an idempotent.