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International Journal of Mathematics and Mathematical Sciences
Volume 2009, Article ID 582181, 8 pages
Research Article

Vanishing Power Values of Commutators with Derivations on Prime Rings

Department of Mathematics, Belda College, Belda, Paschim Medinipur 721424 , India

Received 30 August 2009; Accepted 14 December 2009

Academic Editor: Howard Bell

Copyright © 2009 Basudeb Dhara. 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.


Let ๐‘… be a prime ring of char ๐‘…โ‰ 2, ๐‘‘ a nonzero derivation of ๐‘… and ๐œŒ a nonzero right ideal of ๐‘… such that [[๐‘‘(๐‘ฅ),๐‘ฅ]๐‘›,[๐‘ฆ,๐‘‘(๐‘ฆ)]๐‘š]๐‘ก=0 for all ๐‘ฅ,๐‘ฆโˆˆ๐œŒ, where ๐‘›โ‰ฅ0, ๐‘šโ‰ฅ0, ๐‘กโ‰ฅ1 are fixed integers. If [๐œŒ,๐œŒ]๐œŒโ‰ 0, then ๐‘‘(๐œŒ)๐œŒ=0.