  Let L/K be an extension of number fields where L/\Q is abelian. We define
such an extension to be Leopoldt if the ring of integers O_L of L is free over
the associated order A_L/K. Furthermore we define an abelian number field K to
be Leopoldt if every finite extension L/K with L/Q abelian is Leopoldt in the
sense above. Previous results of Leopoldt, Chan & Lim, Bley, and Byott & Lettl
culminate in the proof that the n-th cyclotomic field Q^(n) is Leopoldt for
every n. In this paper, we generalize this result by giving more examples of
Leopoldt extensions and fields, along with explicit generators.
