Polynomial extensions of cP-Baer rings

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.