Department of Mathematics, Shahed University, Tehran, Iran.
In this paper, we introduce the new notion of n-f-clean rings as a generalization
of f-clean rings. Next, we investigate some properties of such rings. We prove that Mn(R) is
n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of
n-cleanness and n-f-cleanness are equivalent.