On Derivations In Prime Gamma-Near-Rings - Dey, Kalyan Kumar; Paul, Akhil Chandra (GANIT: Journal of Bangladesh Mathematical Society, 2013)
Let N be a non zero-symmetric left ?-near-ring. If N is a prime ?-near-ring with nonzero derivations D1 and D2 such that D1(x)?D2(y) = D2(x)?D1(y) for every x, y?N and ???, then we prove that N is an abelian ?-near-ring. Again if N is a 2-torsion free prime ?-near-ring and D1 and D2 are derivations satisfying D1(x)?D2(y) = D2(x)?D1(y) for every x, y?N and ???, then we prove that D1D2 is a derivation on N if and only if D1 = 0 or D2 = 0. DOI: http://dx.doi.org/10.3329/ganit.v32i0.13642 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 23-28