CENTRALIZERS OF GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS


ALBAŞ E. , ARGAÇ N. , DE FİLİPPİS V.

SIBERIAN MATHEMATICAL JOURNAL, cilt.58, ss.1-10, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 58 Konu: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1134/s0037446617010013
  • Dergi Adı: SIBERIAN MATHEMATICAL JOURNAL
  • Sayfa Sayıları: ss.1-10

Özet

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).