On graded nil good rings

Abstract: In this paper we introduce and study the notion of a graded nil-good ring which is graded by a group. We investigate extensions of graded nil-good rings to graded group rings, Further, we discuss graded matrix ring extensions and trivial extensions of graded nil-good rings. Furthermore, we show that the class of graded rings which are nil-good and the class of graded nil-good rings are not comparable. Moreover, we discuss the question of when the nil-good property of the component, which corresponds to the identity element the grading group, implies that the whole graded ring is graded nil-good is also treated.