On Semiclean Group Rings

摘要

A ring R with unity is called semiclean,if each of its elements is the sum of a unit and a periodic.Every clean ring is semiclean.It is not easy to characterize a semiclean group ring in general.Our purpose is to consider the following question:If G is a locally finite group or a cyclic group of order 3,then when is RG semiclean? Some known results on clean group rings are generalized.