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Abstract
Let N be a 2-torsion free prime near-ring.If N admits a non zero left semi derivation d with g such that (i)d[ x , y ] = 0 (ii) d[ x , y ] = [ x , y ] (iii) d[ x ,y ]= -[ x, y ] (iv) d( x o y) = ( x o y) (v) d( x o y) = - ( x o y) (vi) d[ x , y ] ϵ Z(N) (vii) [d(x) , y] ϵ Z(N) (viii) d(x)oy = xoy (ix) d(x o y) ϵ Z(N) (x) d(x) o y ϵ Z(N) (xi) d(x o y) = [ x , y ] (xii) d [ x , y ] = (x o y), for all x , y ϵN, then N is a commutative ring.
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