Semistar G-GCD domains
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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}.
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}.
참고문헌 (14)
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