Power Bases in Dihedral Quartic Fields Original Research Article

A quartic number field,L, is calleddihedralif the normal closure,N, ofLsatisfies Gal(N/image)congruent withD8. We investigate whether or not the ring of integers of such a quartic field has a power basis. When the quadratic subfield ofLis 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.