Orthogonality of two left and right generalized derivations on ideals in semiprime rings

摘要

In this paper, we present some results concerning orthogonality of l-generalized derivations and r-generalized derivations on ideals in semiprime rings, we also study the connections between orthogonality and some properties of the composition of a l-generalized derivation and a r-generalized derivation. These results are related to results of Bre?ar and Vukman (Rad Mat 5(2):237-246, 1989), that extend a theorem by Posner (ProcAmMath Soc 8:1093-1100,1957) about products of derivations on prime rings.