Strong commutativity preserving biderivations on prime rings
Abstract
In the present paper we investigate the commutativity in a prime ring R which admits biderivation D : R×R → R satisfying [D(x,x),D(y,y)] = [x,y] for all x,y ∈ R. More precisely, we generalize the result of Bell et.al.[3] on strong commutativity preserving biderivations. Moreover, we obtain that generalized biderivation acts as left bimultiplier, whenever it behaves as right R-homomorphisms.
Copyright © 2017 Faiza Shujat, Abu Zaid Ansari, Shahoor Khan. 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, S. Khan, Strong commutativity preserving biderivations on prime rings, J. Math. Comput. Sci. 7 (2017), 230–236.
BibTeX
@article{Shujat2017,
author = {Shujat, Faiza and Ansari, Abu Zaid and Khan, Shahoor},
title = {Strong commutativity preserving biderivations on prime rings},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {230--236},
doi = {}
}