# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Note on the Galois module structure of quadratic extensions

### Tom 67 / 1994

Colloquium Mathematicum 67 (1994), 15-19 DOI: 10.4064/cm-67-1-15-19

#### Streszczenie

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 $ℚ^{(n)}/ℚ^{(n)^+}$.

• Günter Lettl

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek