On commutativity of prime near-rings with multiplicative generalized derivation

Authors : Zeliha BEDİR, Öznur GÖLBAŞI

Pages : 209-221

Doi:10.31801/cfsuasmas.443732

View : 9 | Download : 14

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :In the present paper, we shall prove that 3-prime near-ring N is commutative ring, if any one of the following conditions are satisfied: insert ignore into journalissuearticles values(i); finsert ignore into journalissuearticles values(N);⊆Z, insert ignore into journalissuearticles values(ii); finsert ignore into journalissuearticles values([x,y]);=0, insert ignore into journalissuearticles values(iii); finsert ignore into journalissuearticles values([x,y]);=±[x,y], insert ignore into journalissuearticles values(iv); finsert ignore into journalissuearticles values([x,y]);=±insert ignore into journalissuearticles values(xoy);, insert ignore into journalissuearticles values(v); finsert ignore into journalissuearticles values([x,y]);=[finsert ignore into journalissuearticles values(x);,y], insert ignore into journalissuearticles values(vi); finsert ignore into journalissuearticles values([x,y]);=[x,finsert ignore into journalissuearticles values(y);], insert ignore into journalissuearticles values(vii); finsert ignore into journalissuearticles values([x,y]);=[dinsert ignore into journalissuearticles values(x);,y], insert ignore into journalissuearticles values(viii); finsert ignore into journalissuearticles values([x,y]);=dinsert ignore into journalissuearticles values(x);oyinsert ignore into journalissuearticles values(ix); [finsert ignore into journalissuearticles values(x);,y]∈Z for all x,y∈N where f is a nonzero multiplicative generalized derivation of N associated with a multiplicative derivation d.
Keywords : Prime near ring, derivation, multiplicative generalized derivation