Semistar G-GCD domains
J. Korean Math. Soc. 2019 Vol. 56, No. 6, 1689-1701
https://doi.org/10.4134/JKMS.j180862
Published online November 1, 2019
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
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