Rings in which not invertible elements are uniquely clean
Keywords:strongly clean ring, local ring, uniquely clean ring, group ring
We call a ring R a generalized uniquely clean (or GUC for short) if every not invertible element in R is uniquely clean. Let R be a ring. It is shown that R is GUC if and only if it is a local ring or a uniquely clean ring. Thus the GUC ring is a generalization of the local ring. Some basic properties of GUC rings are proved.