feebly nil-clean matrix rings

In this note, we study some elementary properties of feebly nil-clean rings. a ringr is feebly nil-clean if for any a ∈ r there exist two orthogonal idempotents e, f ∈ r and anilpotent w ∈ r such that a = e − f + w. we prove that if r is a ring of bounded index andj(r) is nil, then mn(r) is feebly nil-clean for any n ∈ n. this characterizes many classes ofrings over which every matrix is sum of orthogonal idempotent and nilpotent matrices.