(untitled) (Communications in Mathematical Research, 2021)
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.