Generalized f-clean rings
Subject Areas : Rings theory
S. Jamshidvand
1
(Department of Mathematics, Shahed University, Tehran, Iran)
H. Haj Seyyed Javadi
2
(Department of Mathematics, Shahed University, Tehran, Iran)
N. Vahedian Javaheri
3
(Department of Mathematics, Shahed University, Tehran, Iran)
Keywords: Full element, clean ring, n-clean ring, n-f-clean ring,
Abstract :
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 $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the definitions of n-cleanness and n-f-cleanness are equivalent.