Address:
* Department of Mathematics, Faculty of Sciences, Mohammed First University, 60000 Oujda, Morocco
** Regional center of Education and Training, 60000 Oujda, Morocco
E-mail:
abdelmalekazizi@yahoo.fr
benamarajamal@hotmail.fr
mcismaili@yahoo.fr
talbimm@yahoo.fr
Abstract: Let $K=\mathbb{Q}(\theta )$ be a pure cubic field, with $\theta ^3=D$, where $D$ is a cube-free integer. We will determine the reduced ideals of the order $\mathcal{O}=\mathbb{Z}[\theta ]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $\lnot \equiv \pm 1(mod 9)$.
AMSclassification: primary 11R16; secondary 11R29, 11T71.
Keywords: cubic field, reduced ideal.
DOI: 10.5817/AM2020-3-171