| On Tame Kernels and Ideal Class Groups |
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| 作者姓名： | Hai Yan ZHOU |
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| 作者单位： | [1]Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China [2]Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097, P. R. China |
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| 基金项目： | Supported by NSFC10571080, SRFDP |
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| 摘 要： | It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI（δE,T） under the action of the Galois group, where E = F（ζp^n ） and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F（ζ3）.
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| 关 键 词： | 理想类群 循环立方域 核心 数学 |
| 修稿时间： | 2005-03-16 |
On Tame Kernels and Ideal Class Groups |
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| Hai Yan ZHOU.On Tame Kernels and Ideal Class Groups[J].Acta Mathematica Sinica,2007,23(10):1807-1812. |
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| Authors: | Hai Yan Zhou |
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| Institution: | (1) Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China;(2) Institute of Mathematics, School of Mathematics and computer Sciences, Nanjing Normal University, Nanjing, 210097, P. R. China |
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| Abstract: | |
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| Keywords: | cyclic cubic fields tame kernels ideal class groups |
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