Korean J. Math. Vol. 24 No. 3 (2016) pp.537-543
DOI: https://doi.org/10.11568/kjm.2016.24.3.537

When the Nagata ring ${D(X)}$ is a sharp domain

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Published: Sep 30, 2016
Keywords:
star operation, sharp domain, polynomial ring, Nagata ring
Mathematics Subject Classification:
13A15, 13F05

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Gyu Whan Chang
Department of Mathematics Education Incheon National University Incheon 22012, Korea

Abstract

Let $D$ be an integral domain, $X$ be an indeterminate over $D$, $D[X]$ be the polynomial ring over $D$, and $D(X)$ be the Nagata ring of $D$. Let $[d]$ be the star operation on $D[X]$, which is an extension of the $d$-operation on $D$ as in [5,Theorem 2.3]. In this paper, we show that $D$ is a sharp domain if and only if $D[X]$ is a $[d]$-sharp domain, if and only if $D(X)$ is a sharp domain.


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