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.Citation
Conrad, M., Replogle D., (2002) 'Nontrivial Galois module structure of cyclotomic fields'. Mathematics of Computation, 72 (242), pp.891 -899Publisher
American Mathematical SocietyJournal
Mathematics of ComputationAdditional Links
http://www.ams.org/journal-getitem?pii=S0025-5718-02-01457-6Type
ArticleLanguage
enISSN
0025-5718ae974a485f413a2113503eed53cd6c53
10.1090/S0025-5718-02-01457-6
Scopus Count
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