  Birkenmeier and Heider, in [2], say that a ring R is right cP-Baer if the
right annihilator of a cyclic projective right R-module in R is generated by an
idempotent. These rings are a generalization of the right p.q.-Baer and abelian
rings. Generally, a formal power series ring over one indeterminate, wherein
its base ring is right p.q.-Baer, is not necessarily right p.q.-Baer. However,
according to [2], if the base ring is right cP-Baer then the power series ring
over one indeterminate is right cP-Baer. Following [2], we investigate the
transfer of the cP-Baer property between a ring R and various extensions
(including skew polynomials, skew Laurent polynomials, skew power series, skew
inverse Laurent series, and monoid rings). We also answer a question posed by
Birkenmeier and Heider [2] and provide examples to illustrate the results.
