Cubic Fields

István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics

Chapter Chapter 8 in Diophantine Equations and Power Integral Bases, 2019, pp 105-111 from Springer

Abstract: Abstract The first nontrivial examples of power integral bases can be found in cubic number fields. In this chapter we briefly summarize the results obtained for computing power integral bases in cubic fields. This is an easy case, just a routine matter, but it has initiated an exciting project, to extend the computations to higher degree fields. In Sect. 8.2 we also involve the infinite parametric family of simplest cubic fields, in which, thanks to the results on the corresponding parametric Thue equations, we can easily determine the generators of power integral bases. Further, in Sect. 8.3 we mention monogenity properties of pure cubic fields.

Date: 2019
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DOI: 10.1007/978-3-030-23865-0_8

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