The Tame Kernel of Multiquadratic Number Fields
The Tame Kernel of Multiquadratic Number Fields
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DOI：
10.1080/00927870802254801
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发表时间：
2009-02
影响因子：
0.7
通讯作者：
Haiyan Zhou
中科院分区：
文献类型：
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作者：
Haiyan Zhou
设F/K是n次数域的Galois扩张，F是F中的整数环，p是不整除n的素数.𝒪设K2表示Milnor K-函子.本文利用F/K的中间域研究F的驯服核K2<$F的奇部结构。特别地，对于多重二次域F，我们将得到K2F的p i -秩，（i > 0）。最后，我们将确定当− 100 < d < 0，d1 = 2，3，5，7时K2<$F的奇数部分的结构。
Let F/K be a Galois extension of a number field of degree n, 𝒪 F the ring of integers in F, and p a prime number which does not divide n. Let K 2 denote the Milnor K-functor. In this article, we shall study the structure of the odd part of the tame kernel K 2𝒪 F of F by using the intermediate fields of F/K. In particular, for a multiquadratic field F, we shall get the p i -rank, (i > 0) of K 2𝒪 F . Finally, we shall determine the structure of the odd parts of K 2𝒪 F when where − 100 < d < 0, d 1 = 2,3,5,7.