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)

Received: 2014-05-09 Accepted : 2014-08-27 Published : 2014-03-01

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.

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