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On the module structure of rings of integers in p-adic number fields over associated orders

Published online by Cambridge University Press:  01 March 1998

Y. MIYATA
Y. MIYATA
Affiliation:
Faculty of Education, Shizuoka University, Ohya Shizuoka 422, Japan
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Abstract

Let p be an odd prime number. Let k be a [pfr ]-number field and [ofr ] the ring of all integers of k with a prime element π. Let K/k be a cyclic extension with Galois group G, and [Afr ] the associated order of the ring [Ofr ] of all integers in K:

[Afr ]={f∈kG[mid ]f[Ofr ]⊆[Ofr ]}.

F. Bertrandias and M-J. Ferton [1] obtained necessary and sufficient conditions that [Ofr ] is [Afr ]-free in the case K/k is of degree p. The purpose of this paper is to study such conditions in case K/k is a cyclic totally ramified Kummer extension of degree n=pm.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 2 , March 1998 , pp. 199 - 212
Copyright
Cambridge Philosophical Society 1998

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