Bulletin of the
Korean Mathematical Society BKMS

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 $R$, $R[[x;\alpha]]$ is right p.p., if and only if $R[[x,x^{-1};\alpha]]$ 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 $I(R)$.

Keywords: Baer rings, right p.p.-rings, $\alpha$-rigid rings, skew power series, Ore extensions

MSC numbers: 16S36, 16E50