Generalized Skew Derivations Cocentralizing Multilinear Polynomials

Abstract

Let R be a prime ring of characteristic different from 2, Q r be its right Martindale quotient ring and C be its extended centroid. Suppose that F, G are generalized skew derivations of R and $${f(x_1, \ldots, x_n)}$$ is a non-central multilinear polynomial over C with n non-commuting variables. If F and G satisfy the following condition: $$F(f(r_1,\ldots, r_n))f(r_1, \ldots,r_n)-f(r_1,\ldots,r_n)G(f(r_1,\ldots, r_n))\in C$$ for all $${r_1, \ldots, r_n \in R}$$ , then we describe all possible forms of F and G.