Semi derivations of prime gamma rings

Abstract

Let M be a prime ?-ring satisfying a certain assumption (*). An additive mapping f : M ? M is a semi-derivation if f(x?y) = f(x)?g(y) + x?f(y) = f(x)?y + g(x)?f(y) and f(g(x)) = g(f(x)) for all x, y?M and ? ? ?, where g : M?M is an associated function. In this paper, we generalize some properties of prime rings with semi-derivations to the prime &Gamma-rings with semi-derivations. 2000 AMS Subject Classifications: 16A70, 16A72, 16A10.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10309GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 65-70