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.
展开▼