Geodesic
Existence and Posner's Theorem for α-derivations in Prime Near-rings
Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 1 
M. S. Samman. Existence and Posner's Theorem for α-derivations in Prime Near-rings. Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2009_78_1_a3/
@article{AMUC_2009_78_1_a3,
     author = {M. S. Samman},
     title = {Existence and {Posner's} {Theorem} for \ensuremath{\alpha}-derivations in {Prime} {Near-rings}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2009},
     volume = {78},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2009_78_1_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper we define α-derivation for near-rings and extend some results for derivations of prime rings or near-rings to a more general case for α-derivations of prime near-rings. To initiate the study of the theory, the existence of such derivation is shown by an example. It is shown that if d is an α-derivation of a prime near-ring N such that d commutes with α, then d 2 = 0 implies d = 0. Also a Posner-type result on the composition of α-derivations is obtained.