The nontriviality of certain Zl-extensions
The nontriviality of certain Zl-extensions
复制标题
某些 Zl 扩展的非平凡性
DOI：
10.1016/0022-314x(74)90034-1
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发表时间：
1974
影响因子：
0.7
通讯作者：
R. Gold
中科院分区：
文献类型：
--
作者：
R. Gold
设k是一个j域，k是k的基本Z -扩展，a0， a分别是k， k的l类群。已知如果A 0 1−J是非平凡的，则A 1 J是无限的。如果将l上的素数所表示的类从两组中分离出来，则证明该结果仍然成立。这适用于k= Q（(−m) 1 2）和a0 =(0)，以获取不变量λ和μ的信息。存在这样的k λ≥2。
Let k be a J-field, K the basic Z l-extension of k, and A 0, A the l-class groups of k, K respectively. It is known that if A 0 1− J is nontrivial, then A 1 J ̄ is infinite. It is shown that this result is still true if the classes represented by the primes lying over l are factored out from both groups. This is applied to k= Q ((− m) 1 2) and A 0=(0) for information on the invariants λ and μ. There are such k for which λ≥ 2.