Commutativity results with derivations on semiprime rings
Abstract
In this paper, let R be a 2-torsion free semiprime ring and U a non-zero ideal of R, d a derivation mapping. If R admitting
A derivation d satisfies one of the following .
(i)[d(x),d(y)]=[x,y] for all x, y in U.
(ii)[d(x)2,d(y)2]=[x ,y] for all x, y in U.
(iii) [d(x) ,d(y)]=[x2,y2 ] for all x, y in U.
(iv)[d(x)2,d(y)2]=[x2,y2] for all x, y in U.
A non – zero derivation d satisfies one of the following:
(i)d([d(x),d(y) ])=[x,y] for all x, y in U.
(ii)d([d(x),d(y)]=[d(x),d(y)] for all x, y in U. Then R contains a non-zero central ideal.
Copyright © 2012 Mehsin Jabel Atteya. 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
M. J. Atteya, Commutativity results with derivations on semiprime rings, J. Math. Comput. Sci. 2 (2012), 853–865.
BibTeX
@article{Atteya2012,
author = {Atteya, Mehsin Jabel},
title = {Commutativity results with derivations on semiprime rings},
journal = {J. Math. Comput. Sci.},
volume = {2},
year = {2012},
pages = {853--865},
doi = {}
}