$$\mathfrak {cP}$$ -Baer Polynomial Extensions

A ring R is called right \(\mathfrak {cP}\)-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 rings and abelian rings. Following Birkenmeier and Heider (Commun Algebra 47(3):1348–1375, 2019 https://doi.org/10.1080/00927872.2018.1506462), we investigate the transfer of the \(\mathfrak {cP}\)-Baer property between a ring R and many polynomial extensions (including skew polynomials, skew Laurent polynomials, skew power series, skew inverse Laurent series), and monoid rings. As a consequence, we answer a question posed by Birkenmeier and Heider (2019).