On the Invariant Factors of Kummer Orders in the Rings of Integers of p-adic Number Fields of Degreep2
On the Invariant Factors of Kummer Orders in the Rings of Integers of p-adic Number Fields of Degreep2
复制标题
论p2阶p进数域整数环中Kummer阶的不变因子
DOI：
10.1006/jnth.1997.2170
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发表时间：
1997
影响因子：
0.7
通讯作者：
Y. Miyata
中科院分区：
文献类型：
--
作者：
Y. Miyata
设K/k是p进数域k上度为2的扩张，其Galois群为G.研究了整数环K的Galois模结构.本文给出了两个扩张的库默阶不变因子Ok在Ok中重合的条件，并给出了两个例子，其中一个例子证明了存在满足D（K）=D（L）的库默扩张K和L，使得Ok和OL不是ZPG-同构的.另一个证明了扩张F和K的存在性，使得在ZpG上O F和O K是同构的，但在O K G上不是。
LetK/kbe an extension of degreep2over a p-adic number fieldkwith the Galois groupG. We study the Galois module structure of the ring OKof integers inK. We determine conditions under which the invariant factors of Kummer orders OKin OKof two extensions coincide with each other and give two examples, one of which shows there exist Kummer extensionsKandLwithD(K)=D(L) such that OKand OLare not ZpG-isomorphic. The other shows the existence of extensionsFandKsuch that OFand OKare isomorphic over ZpGbut not over okG.