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Relative Galois module structure of rings of integers of absolutely Abelian number fields

Henri Johnston
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Abstract

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.

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Henri Johnston. 2007-07-05. Relative Galois module structure of rings of integers of absolutely Abelian number fields. https://arxiv.org/abs/math/0602637

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