Mediterranean Journal of Mathematics

, Volume 13, Issue 5, pp 2397–2424

# Generalized Skew Derivations Cocentralizing Multilinear Polynomials

• Luisa Carini
• Vincenzo De Filippis
• Feng Wei
Article

## 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.

## Keywords

Generalized skew derivation multilinear polynomial prime ring

16W25 16N60

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