ON GENERALIZED(q, f)- REVERSE DERIVATIONS OFPRIME RINGS

Abstract

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 uÎU. 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).