On principally quasi-Baer skew power series rings

Abstract

Let [Formula: see text] be a monomorphism of a ring [Formula: see text] which is not assumed to be surjective. It is shown that, for an [Formula: see text]-weakly rigid [Formula: see text], the skew power series ring [Formula: see text] is right p.q.-Baer if and only if the skew Laurent series ring [Formula: see text] is right p.q.-Baer if and only if [Formula: see text] is right p.q.-Baer and every countable subset of right semicentral idempotents has a generalized countable join.