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

Title:

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

Creator:

Gaál, István and Petrányi, Gábor

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:fa5a86d2-edf0-4d87-a543-17a1d5ae2004
uuid:fa5a86d2-edf0-4d87-a543-17a1d5ae2004

Subject:

simplest quartic field, power integral base, and monogeity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

465-475

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:2

Harvested from:

CDK

Metadata only:

false