Principal Quasi-Baerness of Rings of Skew Generalized Power Series

Abstract

Let $R$ be a ring and $(S, ≤)$ be a strictly totally ordered monoid satisfying that $0 ≤ s$ for all $s ∈ S$. It is shown that if $λ$ is a weakly rigid homomorphism, then the skew generalized power series ring $[[R^{S,≤}, λ]]$ is right p.q.-Baer if and only if $R$ is right p.q.-Baer and any S-indexed subset of $S_r(R)$ has a generalized join in $S_r(R)$. Several known results follow as consequences of our results.