Strong commutativity preserving generalized derivations on multilinear polynomials

Abstract

Let R be a non-commutative prime ring of characteristic different from 2, with right Utumi quotient ring U and extended centroid C and let F and G be generalized derivations of R such that F (x)G(y) − F (y)G(x) = [x, y], for all x, y ∈ S, where S is a subset of R. Here we will discuss the following cases: