ON DERIVATIONS OF PRIME NEAR-RINGS

The near-rings in this letter always stand for zero-symmetric left nor-rings. An additive endomorphism D of a near-ring N is called a derivation on N if D(xy) =xD(y) +D(x)y for all x, y ∈ N. A near-ring N is said to be prime if xNy={0} for x, y ∈ N implies that either x=0 or y=0. Since additions of near-rings are not necessarily commutative, the following Lemma 1 has its own significance.