Commutativity of prime near _ rings
Keywords:
Near-rings, , Prime rings, Generalized derivations, Commutativity, Mathematical proofsAbstract
In this paper, we examine Golbasi’s approach towards the commutativity in prime near-rings with generalized(s,t)- derivations, showing inconsistency in his proof due to its dependence on the implicit assumption of left and right distributivity. To make this proof correct and complete, we provide a more rigorous alternative proof based on a suitable extension of lemma given in [4].
Downloads
References
M. Ashraf, A. Ali and Ali Shakir, ( )- derivations on prime near –rings, Arch Math.(Brno), 40 (2004), 281-286.
Beidar, K. I., Fong, Y and Wang X.K, ‘Posner and Herstein theorems for derivations of 3- prime near rings’.Com. Algebra, 24(5) (1996) 1581-1589
Bell, H.E., Mason, G., ‘ On derivations in near rings’ and near fields, G. Betsch (editor), 137, North – Holland, Amsterdam, 1987, pp. 31-36.
Bell, H. E., ‘On prime near- rings with generalized derivation’ International Journal of Mathematics, Volume 2008.
Gölbasi, Ö., and N. Aydin, ‘Results on prime near- rings with ( )- derivations’ , Math. J. of Okayama Univ., 46, 1-7, (2004
Gölbasi, Ö., ‘ On prime near- rings with Generalized ( )- dervations’ Kyungpook Math. J. 45 (2005), 249-254.
Gölbasi, Ö., ‘Some properties of prime near- rings with ( )- dervations’ Siberian Mathematical Journal, Vol. 46, No. 2, PP. 270 – 275, 2005
Posner, E. C, “Derivations in prime ring”, Porc. Amer. Math. Soc,(1957) 1093-1100
Wang, X.K, ‘ Derivations in prime near- rings’, Proc. Amer. Math. Soc., 121 (1994), 361- 366.
