$\mathfrak{cP}$-Baer skew Hurwitz series rings
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A ring $R$ is said to be right $\mathfrak{cP}$-Baer if the right annihilator of a cyclic projective right $R$-module in $R$ is generated by an idempotent. This class of rings generalizes the class of right p.q.-Baer rings and abelian rings. We study the relationship between the $\mathfrak{cP}$-Baer property of a ring $R$ and those of the skew Hurwitz series ring $R_{H}[[x;\sigma]]$. We also study the necessary and sufficient conditions for the ring $R_{H}[[x;\sigma]]$ to be $APP$.
Abstract
A ring $R$ is said to be right $\mathfrak{cP}$-Baer if the right annihilator of a cyclic projective right $R$-module in $R$ is generated by an idempotent. This class of rings generalizes the class of right p.q.-Baer rings and abelian rings. We study the relationship between the $\mathfrak{cP}$-Baer property of a ring $R$ and those of the skew Hurwitz series ring $R_{H}[[x;\sigma]]$. We also study the necessary and sufficient conditions for the ring $R_{H}[[x;\sigma]]$ to be $APP$.