Relative Galois module structure of rings of integers of absolutely Abelian number fields
| dc.creator | Johnston, Henri | |
| dc.date | 2006-02-27 | |
| dc.date | 2007-07-05 | |
| dc.date.accessioned | 2026-07-07T08:14:03Z | |
| dc.date.available | 2026-07-07T08:14:03Z | |
| dc.description | 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. | |
| dc.description | 18 pages, uses xypic. Completely rewritten following referee's report (note that first version contained serious error). To appear in Crelle | |
| dc.identifier | https://arxiv.org/abs/math/0602637 | |
| dc.identifier | http://arxiv.org/abs/math/0602637 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132986 | |
| dc.subject | Number Theory | |
| dc.subject | 11R33; 11R04 | |
| dc.title | Relative Galois module structure of rings of integers of absolutely Abelian number fields | |
| dc.type | text |