Note on the Galois module structure of quadratic extensions
Volume 67 / 1994
Colloquium Mathematicum 67 (1994), 15-19
DOI: 10.4064/cm-67-1-15-19
Abstract
In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, $ℚ^{(p)}$. For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of $ℚ^{(n)}/ℚ^{(n)^+}$.
