A module M_R is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and M_R be a α-compatible module and T=R[[x;α]]. It is shown that M[[x]]_T is right p.q.-Baer if and only if M_R is right p.q.-Baer and the right annihilator of any countably-generated submodule of M is generated by an idempotent. As a corollary we obtain a generalization of a result of Liu, 2002.

This research is supported by Shahrood University of Technology of Iran.