Characterizations of graded Pru"fer star-multiplication domains
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Let R=bigoplus_alphainGammaR_alpha be a graded integral domain graded by an arbitrary grading torsionless monoid Gamma, and star be a semistar operation on R. In this paper we define and study the graded integral domain analogue of star-Nagata and Kronecker function rings of R with respect to star. We say that R is a graded Pr"ufer star-multiplication domain if each nonzero finitely generated homogeneous ideal of R is star_f-invertible. Using star-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr"uferstar-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a PvMD.
Abstract
Let R=bigoplus_alphainGammaR_alpha be a graded integral domain graded by an arbitrary grading torsionless monoid Gamma, and star be a semistar operation on R. In this paper we define and study the graded integral domain analogue of star-Nagata and Kronecker function rings of R with respect to star. We say that R is a graded Pr"ufer star-multiplication domain if each nonzero finitely generated homogeneous ideal of R is star_f-invertible. Using star-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr"uferstar-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a PvMD.
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