ON GENERALIZED(Ө, Ø)- REVERSE DERIVATIONS OF PRIME RINGS

In this paper we will introduce the concept of (Ө, Ø) reverse derivation, generalized (Ө, Ø) reverse derivation and generalized left (Ө, Ø) derivation. Let R be a 2-torsion free prime ring and U a Lie ideal of R such that u2inU, for all uinU. The main result of this paper states that if F is a generalized (Ө, Ө) reverse derivation on R which also acts as a homomorphism or as anti- homomorphism on U, then either d=0 or UsubseteqZ(R) Further, as an application of this result it is shown that, if every generalized left (Ө, Ө) derivation on R which also acts as a homomorphism or as anti- homomorphism on U, then either d=0 or UsubseteqZ(R).