Commutativity results with derivations on semiprime rings

Mehsin Jabel Atteya

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.

 


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How to Cite this Article:

Mehsin Jabel Atteya, Commutativity results with derivations on semiprime rings, Journal of Mathematical and Computational Science, Vol 2, No 4 (2012), 853-865

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.

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