群环单位猜想的一个反例

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2021-02-23 DOI:10.4007/annals.2021.194.3.9

Giles Gardam

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引用次数: 34

摘要

通常归属于Kaplansky的单位猜想预测，如果$K$是一个域，$G$是一个无扭群，那么群环$K[G]$的唯一单位是平凡单位，即群元素的非零标量倍数。我们举一个具体的反例来说明这个猜想;群实际上是阿贝尔的场是二阶的。

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A counterexample to the unit conjecture for group rings

The unit conjecture, commonly attributed to Kaplansky, predicts that if $K$ is a field and $G$ is a torsion-free group then the only units of the group ring $K[G]$ are the trivial units, that is, the non-zero scalar multiples of group elements. We give a concrete counterexample to this conjecture; the group is virtually abelian and the field is order two.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.