ON GRADED UJ-RINGS

In this paper, graded rings are S-graded rings inducing S, that is, rings whose additive groups can be written as a direct sum of a family of their additive subgroups indexed by a nonempty set S, and such that the product of two homogeneous elements is again a homogeneous element. As a generalization of the recently introduced notion of a UJ-ring, we define a graded UJ-ring. Graded nil clean rings which are graded UJ are described. We also investigate the graded UJ-property under some graded ring constructions.