Experimental Mathematics

Power integral bases in the family of simplest quartic fields

Péter Olajos

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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

Permanent link to this document
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

Keywords
Power integral bases simplest quartic fields index form 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


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