2 research outputs found
Nontrivial Galois module structure of cyclotomic fields
We say a tame Galois field extension with Galois group 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 so that
for each there is a tame Galois field extension of degree so that has
nontrivial Galois module structure. However, the proof does not directly yield
specific primes for a given algebraic number field For any
cyclotomic field we find an explicit so that there is a tame degree
extension with nontrivial Galois module structure