TWO PROPERTIES OF THE POWER SERIES RING

ABSTRACT. For a commutative ring with unity, A, it is proved that the power series ring AX is a PF-ring if and only if for any two countable subsets S and T of A such that S Sann(T), there exists c e ann(T) such that bc b for all b e S. Also it is proved A A that a power series ring AX 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