ON GRADED UJ-RINGS

Abstract

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.

Keywords

• Graded ring
• Jacobson radical
• nil clean ring

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