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Mediterranean Journal of Mathematics

, Volume 13, Issue 5, pp 2397–2424 | Cite as

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 

Mathematics Subject Classification

16W25 16N60 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of MessinaMessinaItaly
  2. 2.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingPeople’s Republic of China

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