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|Paper IPM / M / 13152||
Let R=⊕α ∈ ΓRα be a graded integral domain graded by an arbitrary grading torsionless monoid Γ, and ∗ be a semistar operation on R. In this paper we define and study the graded integral domain analogue of ∗-Nagata and Kronecker function rings of R with respect to ∗. We say that R is a graded Prufer ∗-multiplication domain if each nonzero finitely generated homogeneous ideal of R is ∗f-invertible. Using ∗-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Prufer ∗-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a PvMD.
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