Symmetric skew 4-derivations on prime rings
Abstract
For a ring R with an automorphism α a 4-additive mapping D : R4−→ R is called a skew 4-derivation w.r.t. α if it is a α-derivation of R for each argument. Namely it is always an α-derivation of R for the argument being left once (3) arguments are fixed by (3) elements in R. In the present note, begin with a result of Jung and Park [5], we prove that if a skew 4-derivation D associated with an automorphism α with trace f of a noncommutative prime ring R under suitable torsion condition satisfying [f(x),α(x)] = 0 for all x ∈ I, a nonzero ideal of R, then D = 0.
Copyright © 2014 Faiza Shujat, Abu Zaid Ansari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
F. Shujat, A. Z. Ansari, Symmetric skew 4-derivations on prime rings, J. Math. Comput. Sci. 4 (2014), 649–656.
BibTeX
@article{Shujat2014,
author = {Shujat, Faiza and Ansari, Abu Zaid},
title = {Symmetric skew 4-derivations on prime rings},
journal = {J. Math. Comput. Sci.},
volume = {4},
year = {2014},
pages = {649--656},
doi = {}
}