Let D ⊆ E be an extension of integral domains, Γ a numerical semigroup with Γ ⊊ ℕ0, Γ∗ = Γ ∖{0} and R = D + E[Γ∗]. In this paper, we completely characterize when R is a weakly Krull domain, an AWFD or a GWFD. We also prove that R is never a WFD.
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