ON GENERALIZED(q, f)- REVERSE DERIVATIONS OFPRIME RINGS - Faraj, Anwar (Iraqi Journal of Science, 2024)
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 bea 2-torsion free prime ring and U a Lie ideal of R such that u2ÎU, for all uÎU. Themain result of this paper states that if F is a generalized (q, q) reverse derivation onR which also acts as a homomorphism or as anti- homomorphism on U, then eitherd=0 or UÍZ(R) Further, as an application of this result it is shown that, if everygeneralized left (q, q) derivation on R which also acts as a homomorphism or asanti- homomorphism on U, then either d=0 or UÍZ(R).