Centralizers of generalized skew derivations on multilinear polynomials
- Authors: Albaş E.1, Argaç N.1, De Filippis V.2
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Affiliations:
- Department of Mathematics
- M.I.F.T.
- Issue: Vol 58, No 1 (2017)
- Pages: 1-10
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170902
- DOI: https://doi.org/10.1134/S0037446617010013
- ID: 170902
Cite item
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(x1,..., xn) is a noncentral multilinear polynomial over C with n noncommuting variables. Let f(R) = {f(r1,..., rn): ri ∈ R} be the set of all evaluations of f(x1,..., xn) in R, while A = {[G (f(r1,..., rn)), f(r1,..., rn)]: ri ∈ R}, and let CR(A) be the centralizer of A in R; i.e., CR(A) = {a ∈ R: [a, x] = 0, ∀x ∈ A }. We prove that if A ≠ (0), then CR(A) = Z(R).
About the authors
E. Albaş
Department of Mathematics
Author for correspondence.
Email: emine.albas@ege.edu.tr
Turkey, Bornova, Izmir
N. Argaç
Department of Mathematics
Email: emine.albas@ege.edu.tr
Turkey, Bornova, Izmir
V. De Filippis
M.I.F.T.
Email: emine.albas@ege.edu.tr
Italy, Messina