Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS

  • Sahandi, Parviz (Department of Mathematics University of Tabriz, School of Mathematics Institute for Research in Fundamental Sciences (IPM))
  • Received : 2013.12.18
  • Accepted : 2014.02.02
  • Published : 2014.03.30
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Abstract

Let $R={\bigoplus}_{\alpha{\in}\Gamma}R_{\alpha}$ be a graded integral domain graded by an arbitrary grading torsionless monoid ${\Gamma}$, 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 Pr$\ddot{u}$fer ⋆-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 Pr$\ddot{u}$fer ⋆-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a $P{\upsilon}MD$.

Keywords

Acknowledgement

Supported by : Institute for Research in Fundamental Sciences (IPM)

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