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
842 48 Bratislava, Slovak Republic
Telephone: + 421-2-60295111 Fax: + 421-2-65425882
e-Mail: email@example.com Internet: www.iam.fmph.uniba.sk/amuc
© 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE