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- W266112551 abstract "Abstract. We study ¾ -derivations on reduced near-rings and extend certain results onderivations to ¾ -derivations with some conditions. 1. IntroductionA (left) near-ring is a set with two binary operations + and ¢ such that(i) ( N; +) is a group (not necessarily abelian) with identity 0,(ii) ( N;¢ ) is a semigroup and(iii) for all x;y;z 2 N , x ( y + z ) = xy + xz: Throughout this paper, N will denote a zero symmetric near-ring ( a 0 = 0 a = 0for all a 2 N ) : A derivation d on a near-ring N is an additive endomorphism having d ( xy ) = xd ( y ) + d ( x ) y for all x;y 2 N and a ¾ - derivation d on N is defined tobe an additive endomorphism satisfying the product rule d ( xy ) = ¾ ( x ) d ( y )+ d ( x ) y for all x;y 2 N; where ¾ is an automorphism on N. Posner [7] defined derivationson prime rings. Herstein [3] derived commutativity property of prime rings withderivations. Recently in near-ring theory, Bell, Mason [1], Kamal [4] and Cho [2]researched in prime and semi prime near-rings. A near-ring" @default.
- W266112551 created "2016-06-24" @default.
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- W266112551 date "2007-03-01" @default.
- W266112551 modified "2023-09-27" @default.
- W266112551 title "Note on σ-derivations in Near-rings and Reduced Near-rings" @default.
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