dc.contributor.author | Byott, Nigel P. | |
dc.contributor.author | Carter, James E. | |
dc.contributor.author | Greither, Cornelius | |
dc.contributor.author | Johnston, Henri | |
dc.date.accessioned | 2013-04-17T15:35:50Z | |
dc.date.issued | 2011-01-01 | |
dc.description.abstract | Let G be a finite abelian group. A number field
K is called a Hilbert–Speiser field of type G if, for every tame
G-Galois extension L/K, the ring of integers OL is free as an
OK[G]-module. If OL is free over the associated order AL/K
for every G-Galois extension L/K, then K is called a Leopoldt
field of type G. It is well known (and easy to see) that if K is
Leopoldt of type G, then K is Hilbert–Speiser of type G. We show
that the converse does not hold in general, but that a modified
version does hold for many number fields K (in particular, for
K/Q Galois) when G = Cp has prime order. We give examples
with G = C5 to show that even the modified converse is false
in general, and that the modified converse can hold when the
original does not | |
dc.identifier.citation | Vol. 55 (2), pp. 623 - 639 | en_GB |
dc.identifier.doi | 10.1215/ijm/1359762405 | |
dc.identifier.uri | http://hdl.handle.net/10871/8342 | |
dc.language.iso | en | en_GB |
dc.publisher | University of Illinois | en_GB |
dc.title | On the restricted Hilbert-Speiser and Leopoldt properties | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2013-04-17T15:35:50Z | |
dc.identifier.issn | 0019-2082 | |
dc.description | Copyright © 2011 University of Illinois at Urbana-Champaign, Department of Mathematics | en_GB |
dc.identifier.journal | Illinois Journal of Mathematics | en_GB |
refterms.dateFOA | 2023-09-14T13:06:29Z | |