Power bases in dihedral quartic fields

A quartic number field, L, is called dihedral if the normal closure, N, of L satisfies Gal(N/Q) congruent to D-8. We investigate whether or not the ri ng of integers of such a quartic field has a power basis. When the quadrati c subfield of L is imaginary, the problem is completely solved. When it is real, the same method leads to a solution in many cases. Several numerical illustrations of the method are given. (C) 1999 Academic Press.