Relative Power Integral Bases
István Gaál · Birkhäuser Boston eBooks · 2002
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.