Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric familiy of number fields. In this paper we consider the infinite parametric family of simplest quartic fields $K$ generated by a root $\xi$ of the polynomial $P_t(x)=x^4-tx^3-6x^2+tx+1$, assuming that $t>0$, $t\neq 3$ and $t^2+16$ has no odd square factors. In addition to generators of power integral bases we also calculate the minimal index and all elements of minimal index in all fields in this family

Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

summary:It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric family of number fields. In this paper we consider the infinite parametric family of simplest quartic fields $K$ generated by a root $\xi$ of the polynomial $P_t(x)=x^4-tx^3-6x^2+tx+1$, assuming that $t>0$, $t\neq 3$ and $t^2+16$ has no odd square factors. In addition to generators of power integral bases we also calculate the minimal index and all elements of minimal index in all fields in this family

Minimális indexű elemek a legegyszerűbb negyedfokú számtestek végtelen parametrikus családjában

A dolgozatban meghatározásra kerül a legegyszerűbb negyedfokú számtestek végtelen parametrikus családjában a minimális index, és a minimális index összes eleme.MscAlkalmazott Matematikusg