FIELDS OF INVARIANTS FOR ABELIAN GROUPS
FIELDS OF INVARIANTS FOR ABELIAN GROUPS
复制标题
阿贝尔群的不变量域
DOI：
10.1070/rm1973v028n04abeh001594
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发表时间：
1973
影响因子：
0.9
通讯作者：
V. Voskresenskii
中科院分区：
文献类型：
--
作者：
V. Voskresenskii
线性作用于有限维空间的有限变换群的不变量域的合理性问题有很长的历史，但仍然没有完全解决。然而，对于阿贝尔群的变换最近取得了相当大的进展。结果已经接近确定。在本文中，这些结果的详细调查，并公布了一些事实的第一次。该演示文稿是从统一的观点，并定期使用的技术代数环面。在这方面的问题之一Zagliki讨论。
The question of the rationality of fields of invariants for finite groups of transformations that act linearly on a finite-dimensional space has a long history, but still remains not fully solved. However, for abelian groups of transformations considerable progress has recently been made. The results are already close to definitive.In the present article a detailed survey of these results is given, and a number of facts are published for the first time. The presentation is made from a uniform point of view and uses regularly the techniques of algebraic tori. In this context one of the problems of Zariski is discussed.