Generalized Derivations of Prime Gamma Rings - Dey, Kalyan Kumar; Paul, Akhil Chandra (GANIT: Journal of Bangladesh Mathematical Society, 2014)
Let M be a prime ?-ring satisfying a certain assumption a?b?c = a?b?c for all a, b, c?M and ?, ???, and let I be an ideal of M. Assume that (D, d) is a generalized derivation of M and a?M. If D([x, a]?) = 0 or [D(x), a]? = 0 for all x?I, ? ? ?, then we prove that d(x) = p?[x, a]? for all x?I, ?, ? ? ? or a?Z(M) (the centre of M), where p belongs C(M) (the extended centroid of M). GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 33-39 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17654