Graded m-nil clean ring

Abstract

In this paper, we introduce the concept of graded m-nil clean ring to extend the existing notion of graded nil-clean ring introduced in [10]. We explore fundamental properties of these rings, emphasizing the interplay between the identity component and the graded structure. We investigate certain conditions under which graded group rings, graded matrix rings and graded amalgamated algebras inherit the m-nil clean property from their components. Specifically, we establish sufficient conditions for graded group rings and graded matrix rings over commutative m-nil clean rings to be graded m-nil clean rings.