Nontrivial Galois module structure of cyclotomic fields
| dc.creator | Conrad, Marc | |
| dc.creator | Replogle, Daniel R. | |
| dc.date | 2002-01-17 | |
| dc.date.accessioned | 2026-07-07T04:46:14Z | |
| dc.date.available | 2026-07-07T04:46:14Z | |
| dc.description | We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $\Cal{O}_{L}$ is a free $\Cal{O}_{K}[G]$-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.identifier | https://arxiv.org/abs/math/0201322 | |
| dc.identifier | http://arxiv.org/abs/math/0201322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63252 | |
| dc.subject | Number Theory | |
| dc.title | Nontrivial Galois module structure of cyclotomic fields | |
| dc.type | text |