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http://dx.doi.org/10.11568/kjm.2014.22.1.181

CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS  

Sahandi, Parviz (Department of Mathematics University of Tabriz, School of Mathematics Institute for Research in Fundamental Sciences (IPM))
Publication Information
Korean Journal of Mathematics / v.22, no.1, 2014 , pp. 181-206 More about this Journal
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
semistar operation; Nagata ring; Kronecker function ring; Pr$\ddot{u}$fer domain; graded domain; $P{\upsilon}MD$;
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