CENTRALIZERS OF GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS


ALBAŞ E. , ARGAÇ N. , DE FİLİPPİS V.

SIBERIAN MATHEMATICAL JOURNAL, vol.58, no.1, pp.1-10, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1134/s0037446617010013
  • Title of Journal : SIBERIAN MATHEMATICAL JOURNAL
  • Page Numbers: pp.1-10

Abstract

Let R be a prime ring of characteristic different from 2, let Q be the right Martindale quotient ring of R, and let C be the extended centroid of R. Suppose that G is a nonzero generalized skew derivation of R and f(x (1),..., x (n) ) is a noncentral multilinear polynomial over C with n noncommuting variables. Let f(R) = {f(r (1),..., r (n) ): r (i) is an element of R} be the set of all evaluations of f(x (1),..., x (n) ) in R, while A = {[G (f(r (1),..., r (n) )), f(r (1),..., r (n) )]: r (i) is an element of R}, and let C (R) (A) be the centralizer of A in R; i.e., C (R) (A) = {a is an element of R: [a, x] = 0, for all (x) is an element of A }. We prove that if A not equal (0), then C (R) (A) = Z(R).