Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid, G be a nonzero X-generalized skew derivation of R, and S be the set of the evaluations of a multilinear polynomial f(x1, … , xn) over C with n non-commuting variables. Let u, v∈ R be such that uG(x) x+ G(x) xv= 0 for all x∈ S. Then one of the following statements holds:(a)v∈ C and there exist a, b, c∈ Qr such that G(x) = ax+ bxc for any x∈ R with (u+ v) a= (u+ v) b= 0 ;(b)f(x1,…,xn)2 is central-valued on R and there exists a∈ Qr such that G(x) = ax for all x∈ R with ua+ av= 0. © 2018, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature.

Centralizers of X-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings

De Filippis V.
Primo
;
2018-01-01

Abstract

Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid, G be a nonzero X-generalized skew derivation of R, and S be the set of the evaluations of a multilinear polynomial f(x1, … , xn) over C with n non-commuting variables. Let u, v∈ R be such that uG(x) x+ G(x) xv= 0 for all x∈ S. Then one of the following statements holds:(a)v∈ C and there exist a, b, c∈ Qr such that G(x) = ax+ bxc for any x∈ R with (u+ v) a= (u+ v) b= 0 ;(b)f(x1,…,xn)2 is central-valued on R and there exists a∈ Qr such that G(x) = ax for all x∈ R with ua+ av= 0. © 2018, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature.
2018
File in questo prodotto:
File Dimensione Formato  
comm math stat 6-2018.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 672.51 kB
Formato Adobe PDF
672.51 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3133756
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 4
social impact