On Generalized Regular Local Ring

Authors

  • Zubayda M. Ibraheem University of Mosul
  • Naeema A. Shereef University of Mosul

Keywords:

local, π-regular, exchange rings

Abstract

A ring R is called a generalized Von Neumann regular local ring (GVNL-ring) if for any a∈R, either a or (1-a) is π-regular element. In this paper, we give some characterization and properties of generalized regular local rings. And we studied the relation between generalized regular local rings, Von Neumann regular rings, Von Neumann regular local rings (VNL-rings) and exchange rings.

Author Biographies

Zubayda M. Ibraheem, University of Mosul

Dept. Of Mathematics ,College of Computer and   mathematical  Sciences, University of Mosul, Iraq.

Naeema A. Shereef, University of Mosul

Dept. Of Mathematics ,College of Computer and   mathematical  Sciences, University of Mosul, Iraq

References

Burton, D.m.(1970), " A first Course in Rings and Ideals, " Addison Wesley Pulishing Company.
CHEN W.X., TONG W.T. (2006), " On non-commutative VNL-rings and GVNL-rings "(J).Glasgow Math J, 48:11-17.
CONTESSA M. (1984), " On certain classes of pm-rings"(J).Comm. Algebra, , 12:1447-1469.
Mc Coy, N.H.(1939)," Ggeneralized regular rings", Bull.Amer.Math.Soc.Vol.45, pp.175-178.
NICHOLSON.W.K. (1977), " Llifting idempotents and exchange rings". Transacati -ons of the American Math. Society, vol.229, pp.269-278.
Sh.A.Safarisabet and Marzieh. Farmani , ( 2013), " Strongly commuting regular rings" J.Basic .Appl.Sci. Res.3(1) vol 3(1), pp.707-713 .
Von Neumman, J.(1936), " On regular rings". Proc. Nat. Scad. Sciences U.S.A, Vol, 22, pp.707-713.
YING Zhi-ling, (2011), " Some Charactrizations of GVNL_Rings", Journal of Nanjing University of Posts and Telecommunications (Natural Science), Vol.31 No.5

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Published

2015-06-30

How to Cite

Ibraheem, Z. M., & Shereef, N. A. (2015). On Generalized Regular Local Ring. Science Journal of University of Zakho, 3(1), 145–152. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/120

Issue

Vol. 3 No. 1 (2015): June, 2015

Section

Science Journal of University of Zakho

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