The D+E[Γ*] construction from Prüfer domains and GCD-domains

摘要

Let D{subset of with not equal to}E denote an extension of integral domains, Γ be a nonzero torsion-free grading monoid with Γ∩-Γ={0}, Γ*=Γ{set minus}{0} and D+E[Γ*]={f∈E[Γ]|f(0)∈D}. In this paper, we give a necessary and sufficient criteria for D+E[Γ*] to be a Prüfer domain or a GCD-domain.