On power integral bases of certain pure number fields defined by $x^{84}-m$
نویسندگان
چکیده
Let $K$ be a pure number field generated by complex root of monic irreducible polynomial $F(x)=x^{60}-m\in \mathbb{Z}[x]$, with $m\neq \pm1$ square free integer. In this paper, we study the monogeneity $K$. We prove that if $m\not\equiv 1\md{4}$, \mp 1 \md{9} $ and $\overline{m}\not\in\{\mp 1,\mp 7\} \md{25}$, then is monogenic. But $m\equiv \mp1 \md{9}$, or 1\md{25}$, not Our results are illustrated examples.
منابع مشابه
On Power Bases in Number Fields
We survey the problem of existence and computation of power bases in number fields.
متن کاملComputing all power integral bases in orders of totally real cyclic sextic number fields
An algorithm is given for determining all power integral bases in orders of totally real cyclic sextic number fields. The orders considered are in most cases the maximal orders of the fields. The corresponding index form equation is reduced to a relative Thue equation of degree 3 over the quadratic subfield and to some inhomogeneous Thue equations of degree 3 over the rationals. At the end of t...
متن کاملIntegral Bases for Number Fields Arising from Circulant Matrices
In this paper we compute integral bases for some algebraic number fields. Mathematics Subject Classification: 11R04, 11R09, 11S15
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista De La Union Matematica Argentina
سال: 2023
ISSN: ['0041-6932', '1669-9637']
DOI: https://doi.org/10.33044/revuma.2836