On near-rings with two-sided a-derivations

Authors : Nurcan ARGAÇ

Pages : 195-204

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we introduce the notion of two-sided a-derivation of a near-ring and give some generalizations of [1]. Let N be a near ring. An additive mapping f: N\rightarrow N is called an { \it insert ignore into journalissuearticles values(a, b);-derivation } if there exist functions a,b : N\rightarrow N such that finsert ignore into journalissuearticles values(xy);=finsert ignore into journalissuearticles values(x);ainsert ignore into journalissuearticles values(y);+b insert ignore into journalissuearticles values(x);finsert ignore into journalissuearticles values(y); for all x,y\in N. An additive mapping d:N\rightarrow N is called a two-sided a-derivation if d is an insert ignore into journalissuearticles values(a,1);-derivation as well as a insert ignore into journalissuearticles values(1,a);-derivation. The purpose of this paper is to prove the following two assertions: insert ignore into journalissuearticles values(i); Let N be a semiprime near-ring, I be a subset of N such that 0\in I, IN\subseteq I and d be a two-sided a-derivation of N. If d acts as a homomorphism on I or as an anti-homomorphism on I under certain conditions on a, then dinsert ignore into journalissuearticles values(I);= {0}. insert ignore into journalissuearticles values(ii); Let N be a prime near-ring, I be a nonzero semigroup ideal of N, and d be a insert ignore into journalissuearticles values(a, 1);-derivation on N. If d+d is additive on I, then insert ignore into journalissuearticles values(N,+); is abelian.
Keywords : Prime near ring, semiprime near ring, a, 1, derivation, 1, a, derivation, two sided a derivation