群环单位群的Karpilovsky问题

On Karpilovsky's Problem Concerning the Units Groups of Group Rings

Karpilovsky提出如下研究问题:找出R为Noether环时交换群环RG的单位群U(RG)有限生成的充要条件。本文对R为半局部环情形解决了该问题,并得到了Ch.R=p^n,G为p-群时,U(RG)有限生成的充要条件。

Karpilovsky posed the following question:find necessary and safficient conditions for U(RG)to be finitely generated for commutative group ring RG over noetherian ring R.In this note,We solved the problem under the condition that R is semilocal ring.We also get a necessary and sufficient condition of finite generation of U(RG)when Ch.R=p^n and G being a P-group.