Nontrivial Galois module structure of cyclotomic fields
| dc.contributor.author | Conrad, Marc | en_GB |
| dc.contributor.author | Replogle, Daniel R. | en_GB |
| dc.date.accessioned | 2013-04-07T21:47:07Z | |
| dc.date.available | 2013-04-07T21:47:07Z | |
| dc.date.issued | 2002 | |
| dc.identifier.citation | Conrad, M., Replogle D., (2002) 'Nontrivial Galois module structure of cyclotomic fields'. Mathematics of Computation, 72 (242), pp.891 -899 | en_GB |
| dc.identifier.issn | 0025-5718 | |
| dc.identifier.doi | 10.1090/S0025-5718-02-01457-6 | |
| dc.identifier.uri | http://hdl.handle.net/10547/279224 | |
| dc.description.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. | |
| dc.language.iso | en | en |
| dc.publisher | American Mathematical Society | en_GB |
| dc.relation.url | http://www.ams.org/journal-getitem?pii=S0025-5718-02-01457-6 | en_GB |
| dc.subject | cyclotomic units | en_GB |
| dc.subject | Galois module structure | en_GB |
| dc.title | Nontrivial Galois module structure of cyclotomic fields | en |
| dc.type | Article | en |
| dc.contributor.department | Southampton Institute | en_GB |
| dc.contributor.department | College of Saint Elizabeth, New Jersey | en_GB |
| dc.identifier.journal | Mathematics of Computation | en_GB |
| html.description.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. |
