2.50
Hdl Handle:
http://hdl.handle.net/10547/279224
Title:
Nontrivial Galois module structure of cyclotomic fields
Authors:
Conrad, Marc; Replogle, Daniel R.
Abstract:
We say a game Galois field extension L/K with Galois group G has trivial Galois module structure if the rings of integers have the property that OL is a free OK[G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes l so that for each there is a tame Galois field extension of degree l so that L/K has nontrivial Galois module structure. However, the proof does not directly yield specific primes l for a given algebraic number field K. For K any cyclotomic field we find an explicit l so that there is a tame degree l extension L/K with nontrivial Galois module structure.
Affiliation:
Southampton Institute; College of Saint Elizabeth, Morristown, New Jersey
Citation:
Conrad, M., Replogle D., (2002) 'Nontrivial Galois module structure of cyclotomic fields'. Mathematics of Computation, 72 (242), pp.891 -899
Publisher:
American Mathematical Society
Journal:
Mathematics of Computation
Issue Date:
2002
URI:
http://hdl.handle.net/10547/279224
DOI:
10.1090/S0025-5718-02-01457-6
Additional Links:
http://www.ams.org/journal-getitem?pii=S0025-5718-02-01457-6
Type:
Article
Language:
en
ISSN:
0025-5718
Appears in Collections:
Centre for Research in Distributed Technologies (CREDIT)

Full metadata record

DC FieldValue Language
dc.contributor.authorConrad, Marcen_GB
dc.contributor.authorReplogle, Daniel R.en_GB
dc.date.accessioned2013-04-07T21:47:07Z-
dc.date.available2013-04-07T21:47:07Z-
dc.date.issued2002-
dc.identifier.citationConrad, M., Replogle D., (2002) 'Nontrivial Galois module structure of cyclotomic fields'. Mathematics of Computation, 72 (242), pp.891 -899en_GB
dc.identifier.issn0025-5718-
dc.identifier.doi10.1090/S0025-5718-02-01457-6-
dc.identifier.urihttp://hdl.handle.net/10547/279224-
dc.description.abstractWe say a game Galois field extension L/K with Galois group G has trivial Galois module structure if the rings of integers have the property that OL is a free OK[G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes l so that for each there is a tame Galois field extension of degree l so that L/K has nontrivial Galois module structure. However, the proof does not directly yield specific primes l for a given algebraic number field K. For K any cyclotomic field we find an explicit l so that there is a tame degree l extension L/K with nontrivial Galois module structure.en_GB
dc.language.isoenen
dc.publisherAmerican Mathematical Societyen_GB
dc.relation.urlhttp://www.ams.org/journal-getitem?pii=S0025-5718-02-01457-6en_GB
dc.rightsArchived with thanks to Mathematics of Computationen_GB
dc.subjectcyclotomic unitsen_GB
dc.subjectGalois module structureen_GB
dc.titleNontrivial Galois module structure of cyclotomic fieldsen
dc.typeArticleen
dc.contributor.departmentSouthampton Instituteen_GB
dc.contributor.departmentCollege of Saint Elizabeth, Morristown, New Jerseyen_GB
dc.identifier.journalMathematics of Computationen_GB
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