ON SYMMETRIC GENERALIZED 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 2,  2009, pp.203-217
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.2.203
Title & Authors
ON SYMMETRIC GENERALIZED 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS
Park, Kyoo-Hong; Jung, Yong-Soo;

Abstract
In this note, we introduce a symmetric generalized 3-derivation in near-rings and investigate some conditions for a nearring to be a commutative ring.
Keywords
prime near-ring;commutative ring;symmetric 3-derivation;symmetric generalized 3-derivation;
Language
English
Cited by
References
1.
M. Ashraf, A. Ali and S. Ali, $({\sigma},{\tau})$-derivations on prime near-rings, Archivum Mathematicum (BRNO), Tomus. 40 (2004), 281-286.

2.
H.E. Bell, On prime near-rings with generalized derivation, Internat. J. Math. & Math. Sci. 2008 (2008), 1-5.

3.
H.E. Bell and G. Mason, On derivations in near-rings, in Near-Rings and Near-Fields (Tubingen, 1985), G. Betsch, Ed., vol, 137 of North-Holland Mathematics Studies, pp. 31-35, North-Holland, Amsterdam, The Netherlands, 1987.

4.
M. Bresar, On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93.

5.
M. Bresar, Commuting mops: a survey, Taiwanese J. Math. 8(3) (2004), 361-397.

6.
Y. Ceven and M.A. Ozturk, Some properties of symmetric bi-$({\sigma},{\tau})$-derivations in near-rings, Commun. Korean Math. Soc. 22(4) (2007), 487-491.

7.
O. Golbasi, On prime near-rings with generalized $({\sigma},{\tau})$-derivations, Kyungpook Mach. J. 45 (2005), 249-254.

8.
O. Golbasi, Notes on prime near-rings with generalized derivation, Southeast Asian Bull. Math. 30(1) (2006), 49-54.

9.
B. Hvala, Generalized derivations in prime rings, Comm. Aigebra., 26(4) (1998), 1147-1166.

10.
G. Pilz, Near-rings, 2nd Ed. North Holland, Amsterdam, 1983.

11.
E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.

12.
M.A. Quadri, M.S. Khan and N. Rehman, Generalized derivations and commutativity of prime rings, Indian J. pure appl. Math. 34(9) (2003), 1393-1396.

13.
P. Ribenboim, Higher order derivations of modules, Portgaliae Math. 39 (1980), 381-397.

14.
M. Uckun and M.A. Ozturk, On trace of symmetric bi-gamma-derivations in gamma-near-rings, Houston J. Math. 33(2) (2007), 323-339.

15.
J. Vukman, Symmetric bi-derivations on prime and semi-prime rings, Aequationes Math. 38 (1989), 245-254.

16.
J. Vukman, Two results concerning symmetric bi-derivations on prime rings, Aequationes Math. 40 (1990), 181-189.