## Experimental Mathematics

### Power integral bases in the family of simplest quartic fields

Péter Olajos

#### Abstract

Several authors have considered the infinite parametric family of simplest quartic fields $K_t=\mathbb Q(\xi)$. In this paper, we explicitly give all generators of power integral bases in the ring of integers $\mathbb Z_K$ of$K_t$ assuming that $t^2+16$is not divisible by an odd square. We use a well known general algorithm for calculating power integral bases in quartic fields.

#### Article information

Source
Experiment. Math., Volume 14, Issue 2 (2005), 129-132.

Dates
First available in Project Euclid: 30 September 2005

https://projecteuclid.org/euclid.em/1128100125

Mathematical Reviews number (MathSciNet)
MR2169516

Zentralblatt MATH identifier
1092.11042

Subjects
Primary: 11D57: Multiplicative and norm form equations
Secondary: 11Y50: Computer solution of Diophantine equations

#### Citation

Olajos, Péter. Power integral bases in the family of simplest quartic fields. Experiment. Math. 14 (2005), no. 2, 129--132. https://projecteuclid.org/euclid.em/1128100125