Principal Quasi-Baerness of Rings of Skew Generalized Power Series (Communications in Mathematical Research, 2021)
Let $R$ be a ring and $(S, ≤)$ be a strictly totally ordered monoid satisfyingthat $0 ≤ s$ for all $s ∈ S$. It is shown that if $λ$ is a weakly rigid homomorphism, thenthe 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.