Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2019; 56(6): 1689-1701

Online first article July 17, 2019      Printed November 1, 2019

https://doi.org/10.4134/JKMS.j180862

Copyright © The Korean Mathematical Society.

Semistar G-GCD domains

Wafa Gmiza, Sana Hizem

University of Monastir 5000; University of Monastir 5000

Abstract

Let $\star$ be a semistar operation on the integral domain $D$. In this paper, we prove that $D$ is a G-$\widetilde{\star}$-GCD domain if and only if $D[X]$ is a G-$\star_1$-GCD domain if and only if the Nagata ring of $D$ with respect to the semistar operation $\widetilde{\star}$, $Na(D, \star_f)$ is a G-GCD domain if and only if $Na(D, \star_f)$ is a GCD domain, where $\star_1$ is the semistar operation on $D[X] $ introduced by G. Picozza \cite{Picozza}.

Keywords: semistar operation, star operation, polynomial ring, Nagata ring

MSC numbers: 13F20, 13G05, 13A15, 13E99