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Nontrivial Galois module structure of cyclotomic fields

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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.

Publication Information

Output type

Research Output:
Contribution to journal
Article
 Peer-review

Original language

English

Pages from-to (Number of pages)

Pages 891-899

Journal (Volume, Issue Number)

Mathematics of Computation (Volume 72, Issue 242)

Publication milestones

  • Published - 01/01/2002

Publication status

Published - 01/01/2002

ISSN

0025-5718

Publication IDs

  • handle.net: 10547/279224
  • Scopus: 0037376132

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