SOME PROPERTIES OF SYMMETRIC BI-(σ, Τ)-DERIVATIONS IN NEAR-RINGS

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Ceven, Yilmaz (Department of Mathematics Faculty of Arts and Sciences Suleyman Demirel University) ;
Ozturk, Mehmet Ali (Department of Mathematics Faculty of Arts and Sciences Cumhuriyet University)

In this paper, we introduce a symmetric $bi-({\sigma},\;{\tau})-derivation$ in a near-ring and generalize some of the results in [5, 6, 8, 9].

M. Ashraf, A. Ali, and S. Ali, Some properties of prime near-rings with $({\sigma},{\tau})$ -derivation on prime near-rings, Archivum Mathematicum (BRNO), Tornus 40 (2004), 281-286
H. E. Bell and G. Mason, On derivations in near-ring, near-rings and near-fields, NorthHolland, Math. Studies 137 (1987), 31-35
O. Golbasi, Some properties of prime near-rings with $({\sigma},{\tau})$ -derivation, Siberian Mathematical Journal 46 (2005), no. 2, 270-275 https://doi.org/10.1007/s11202-005-0027-9
G. Maksa, On the trace of symmetric bi-derivations, C. R. Math. Rep. Sci. Canada 9 (1987), 303-307
M. A. Oztiirk and Y. B. Jun, On generalized symmetric bi-derivations in prime-rings, East asian Math. J. 15 (1999), no. 2, 165-176
M. A. Oztiirk and Y. B. Jun, On trace of symmetric bi-derivations in near-rings, Inter. J. Pure and Appl. Math. 17 (2004), no. 1, 95-102
G. Pilz, Near-Rings, Second Edition, North-Holland, Amsterdam, 1983
M. Sapanci, M. A. Ozt iirk, and Y. B. Jun, Symmetric bi-derivations on prime rings, East Asian Math. J. 15 (1999), no. 1, 105-109
J. Vukrnan, Symmetric bi-derivations on prime and semi-prime rings, Aequationes Math. 38 (1989), 245-254 https://doi.org/10.1007/BF01840009
X. K. Wang, Derivations in prime near-rings, Proc. Amer. Math. Soc. 121 (1994), no. 2,361-366 https://doi.org/10.2307/2160409

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