Korean J. Math.  Vol 22, No 1 (2014)  pp.181-206
DOI: https://doi.org/10.11568/kjm.2014.22.1.181

Characterizations of graded Prufer $\star$-multiplication domains

Parviz sahandi

Abstract


Let $R=\bigoplus_{\alpha\in\Gamma}R_{\alpha}$ 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 Prufer $\star$-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 Prufer $\star$-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a P$v$MD.


Subject classification

13A15, 13G05, 13A02.

Sponsor(s)

This research was supported by a grant from Institute for Research in Fundamen- tal Sciences (IPM) (No. 91130030).

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