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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.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/18995.html} }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.