Ore extensions of Baer and p.p.-rings

We investigate Ore extensions of Baer rings and p.p.-rings. Let α be an endomorphism and δ an α-derivation of a ring R. Assume that R is an α-rigid ring. Then (1) R is a Baer ring if and only if the Ore extension R[x;α,δ] is a Baer ring if and only if the skew power series ring R[[x;α]] is a Baer ring, (2) R is a p.p.-ring if and only if the Ore extension R[x;α,δ] is a p.p.-ring.