Power integral bases in a family of sextic fields with quadratic subfields

In: Tatra Mountains Mathematical Publications, vol. 64, no. 3

István Gaál - László Remete

Detaily:

Rok, strany: 2015, 59 - 66

Kľúčové slová:

sextic fields, relative cubic extension, power integral basis, relative power integral basis

O článku:

Let $M=\Q(i\sqrt{d})$ be any imaginary quadratic field with a positive square-free $d$. Consider the polynomial \[ f(x)=x³-ax²-(a+3)x-1 \] with a parameter $a\in\Z$. Let $K=M(α)$, where $α$ is a root of $f$. This is an infinite parametric family of sextic fields depending on two parameters, $a$ and $d$. Applying relative Thue's equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields.

Ako citovať:

ISO 690:

Gaál, I., Remete, L. 2015. Power integral bases in a family of sextic fields with quadratic subfields. In Tatra Mountains Mathematical Publications, vol. 64, no.3, pp. 59-66. 1210-3195.

APA:

Gaál, I., Remete, L. (2015). Power integral bases in a family of sextic fields with quadratic subfields. Tatra Mountains Mathematical Publications, 64(3), 59-66. 1210-3195.