A prime decomposition symbol for a non-abelian central extension which is abelian over a bicyclic biquadratic field
A prime decomposition symbol for a non-abelian central extension which is abelian over a bicyclic biquadratic field
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非阿贝尔中心扩张的素数分解符号，该中心扩张在双环双二次域上是阿贝尔的
DOI：
10.1017/s0027763000018948
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发表时间：
1980
影响因子：
0.8
通讯作者：
Yoshiomi Furuta
中科院分区：
文献类型：
--
作者：
Yoshiomi Furuta
在之前的论文 [6] 中，我们对有理数域 Q 上的某些非交换扩展中的素数分解有一些标准，并且作为其特殊情况，我们有双二次留数符号的倒数。互易性是通过对 Q 上的中心扩展使用素数分解的下降法获得的，Q 是双二次域上的阿贝尔式。在本文中，我们一般研究双二次域上的情况。我们定义一个符号[d 1, d 2, p]来表示有理素数p在上述中心扩张中的分解规律。
In a previous paper [6] we had some criteria for the prime decomposition in certain non-abelian extensions over the rational number field Q , and as its special case we had a reciprocity of the biquadratic residue symbol. The reciprocity was obtained by using a descent method of the prime decomposition for a central extension over Q which is abelian over a biquadratic field In the present paper we study on the case over a biquadratic field in general. We define a symbol [d 1, d 2, p] which expresses the decomposition law of a rational prime p in a central extension mentioned above.