On Generalized Regular Local Ring
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.
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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