On Graded $2$-Nil-Good Rings

Emil Ilić-Georgijević

In this paper we introduce and study the notion of a graded $2$-nil-good ring which is graded by a group. We discuss graded group ring and graded matrix ring extensions of graded $2$-nil-good rings. The question of when the $2$-nil-good property of the component, which corresponds to the identity element of the grading group, implies the graded $2$-nil-good property of the whole graded ring is also examined.