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Siberian Mathematical Journal

, Volume 53, Issue 6, pp 1051–1060 | Cite as

Centralizers of generalized derivations on multilinear polynomials in prime rings

  • L. CariniEmail author
  • V. De Filippis
Article

Abstract

Let R be a prime ring of characteristic different from 2, with Utumi quotient ring U and extended centroid C, δ a nonzero derivation of R, G a nonzero generalized derivation of R, and f(x 1, …, x n ) a noncentral multilinear polynomial over C. If δ(G(f(r 1, …, r n ))f(r 1, …, r n )) = 0 for all r 1, …, r n R, then f(x 1, …, x n )2 is central-valued on R. Moreover there exists aU such that G(x) = ax for all xR and δ is an inner derivation of R such that δ(a) = 0.

Keywords

prime ring differential identities generalized derivations 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.University of MessinaMessinaItaly

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