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Relative Power Integral Bases

In: Diophantine Equations and Power Integral Bases

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  • István Gaál

    (University of Debrecen, Institute of Mathematics and Informatics)

Abstract

In this chapter we open a new horizon by considering the problem of power integral bases in relative extensions instead of over ℚ as in the classical situation. The algorithms for determining generators of relative power integral bases will be applied for finding generators of integral bases in higher degree fields having subfields. It is easy to see that if an element generates a power integral basis, then it also generates a relative power integral basis over a subfield. Thus, for example the algorithm for relative quartic extensions described in Section 9.3 will be used in octic fields with a quadratic subfield in Section 10.1.

Suggested Citation

  • István Gaál, 2002. "Relative Power Integral Bases," Springer Books, in: Diophantine Equations and Power Integral Bases, chapter 9, pages 113-127, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0085-7_9
    DOI: 10.1007/978-1-4612-0085-7_9
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