On generalized (θ, ø)‎-reverse derivations of prime rings

الملخص EN

In this paper we will introduce the concept of (q, f) reverse derivation, generalized (q, f) reverse derivation and generalized left (q, f) derivation.

Let R be a 2-torsion free prime ring and U a Lie ideal of R such that u2ÎU, for all unit.

The main result of this paper states that if F is a generalized (q, q) reverse derivation on R which also acts as a homomorphism or as anti- homomorphism on U, then either d = 0 or UÍZ (R) Further, as an application of this result it is shown that, if every generalized left (q, q) derivation on R which also acts as a homomorphism or as anti- homomorphism on U, then either d = 0 or UÍZ (R).