Skew power series extensions of $alpha$-rigid p.p.-rings

摘要

We investigate skew power series of $lpha$-rigid p.p.-rings, where $lpha$ is an endomorphism of a ring $R$ which is not assumed to be surjective. For an $lpha$-rigid ring $R$, $R[[x;lpha]]$ is right p.p., if and only if $R[[x,x^{-1};lpha]]$ 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 $I(R)$.