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Existence and Posner's Theorem for α-derivations
in Prime Near-rings
M. S. Samman
Received: September 18, 2007; Accepted: March 10, 2008
Abstract. 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 d2 = 0 implies d = 0. Also a Posner-type result on the composition of α-derivations is obtained.
Keywords: Derivation; α-derivation; near-ring; prime near-ring; automorphism.
AMS Subject classification: Primary: 16Y30.
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