We investigate skew power series of $alpha$-rigid p.p.-rings, where $alpha$ is an endomorphism of a ring R which is not assumed to be surjective. For an $alpha$-rigid ring R, R[[${chi};{alpha}$]] is right p.p., if and only if R[[${chi},{chi}^{-1};{alpha}$]] is right p.p., if and only if R is right p.p. and any countable family of idempotents in R has a join in I(R).