Some remarks on Hilbert-Speiser and Leopoldt fields of given type

• Autorzy: James E. Carter
• Języki publikacji: EN

Abstrakty

EN

Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers $O_{L}$ in L is free as a module over the associated order $𝓐_{L/K}$. We also give examples, some of which show that this result can still hold without the assumption that K contains a primitive pth root of unity.

Kategorie tematyczne

• 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 2
• Strony: 217-223

Daty

wydano

2007

Twórcy

autor

James E. Carter

• Department of Mathematics, College of Charleston, 66 George Street, Charleston, SC 29424-0001, U.S.A.

Identyfikatory

DOI

10.4064/cm108-2-5