ON GRADED UJ-RINGS

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International Electronic Journal of Algebra
Volume:28 Issue:28
ON GRADED UJ-RINGS

ON GRADED UJ-RINGS

Authors : Emil ILICGEORGIJEVIC

Pages : 193-205

Doi:10.24330/ieja.768259

View : 12 | Download : 8

Publication Date : 2020-07-14

Article Type : Research Paper

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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