p. 37 - 42 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 d^{2} = 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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