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Paper   IPM / M / 13152
School of Mathematics
  Title:   Characterizations of graded Prufer ∗-multiplication domains
  Author(s):  Parviz Sahandi
  Status:   Published
  Journal: Korean J. Math.
  Vol.:  22
  Year:  2014
  Pages:   181-206
  Supported by:  IPM
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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