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SEMISTAR G-GCD DOMAIN

  • Gmiza, Wafa (Department of Mathematics Faculty of sciences University of Monastir) ;
  • Hizem, Sana (Department of Mathematics Faculty of sciences University of Monastir)
  • Received : 2018.12.20
  • Accepted : 2019.04.01
  • Published : 2019.11.01

Abstract

Let ${\star}$ be a semistar operation on the integral domain D. In this paper, we prove that D is a $G-{\tilde{\star}}-GCD$ 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 ${\tilde{\star}}$, $Na(D,{\star}_f)$ 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 [12].

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