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 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. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |