Generalized f-clean rings

Subject Areas : Rings theory

S. Jamshidvand ¹ , H. Haj Seyyed Javadi ² , N. Vahedian Javaheri ³

1 - Department of Mathematics, Shahed University, Tehran, Iran
2 - Department of Mathematics, Shahed University, Tehran, Iran
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.

References:

[1] P. Ara, The exchange property for purely ifinite simple rings, Proc. Amer. Math. Soc, 132, No. 9, (2004) 2543-2547.

 

[2] P. Ara, K. R. Goodearl, and E. Pardo, K0 of purely ifinite simple regular rings, K-Theory, 26, No. 1, (2002) 69-100.

 

[3] V. P. Camillo and H. P. Yu, Exchange rings, units and idempotents, Comm. Algebra, 22, N0. 12, (1994) 4737-4749.

 

[4] H. Chen and Morita Contexts with many units, Algebra, 30, No. 3, (2002) 1499-1512.

 

[5] A. Haghany, Hopficity and co-Hopfisity for Morita Contexts, Comm. Algebra, 27, (1), (1999) 477-492.

 

[6] B. Li and L. Feng, f-clean rings and rings having many full elements, J. Korean Math. Soc, 47, (2010) 247-261.

 

[7] W. K. Nicholson, Liftig Idempotents and exchang rings, Trans. Amer. Math. Soc, 229, (1977) 269-278.

 

[8] G. Xiao and W. Tong, n-clean rings and weakly unit stable range rings,Comm. Algebra, 33, No. 5, (2005)

1501-1517.

 

[9] H. Yu, On quasi-duo rings, Glasgow Math. J, 37, No. 1, (1995) 21-31.