On the module structure of rings of integers in p-adic number fields over associated orders
On the module structure of rings of integers in p-adic number fields over associated orders
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关联阶上 p 进数域中整数环的模结构
DOI：
10.1017/s0305004197002016
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发表时间：
1998
影响因子：
0.8
通讯作者：
Y. Miyata
中科院分区：
文献类型：
--
作者：
Y. Miyata
设p是奇素数。设k是[pfr]-数域，[ofr]是k的素元为π的所有整数环。设K/k是具有Galois群G的循环扩张，[afr]是K中所有整数的环[ofr]的关联阶：[afr]={f∈kg[MID]f[ofr]⊆[ofr]}.F.贝特兰迪亚斯和M-J。Ferton在文[1]中得到了当K/k是p次时，[OFR]无[AFR]的充要条件.本文的目的是研究当K/k是n=Pm次的循环全分枝Kummer扩张时的这种条件.
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.