Vanishing Power Values of Commutators with Derivations on Prime Rings

Basudeb Dhara

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-8

Abstract:

Let 𠑅 be a prime ring of char 𠑅 ≠2 , 𠑑 a nonzero derivation of 𠑅 and 𠜌 a nonzero right ideal of 𠑅 such that [ [ 𠑑 ( 𠑥 ) , 𠑥 ] 𠑛 , [ 𠑦 , 𠑑 ( 𠑦 ) ] 𠑚 ] 𠑡 = 0 for all 𠑥 , 𠑦 ∈ 𠜌 , where 𠑛 ≥ 0 , 𠑚 ≥ 0 , 𠑡 ≥ 1 are fixed integers. If [ 𠜌 , 𠜌 ] 𠜌 ≠0 , then 𠑑 ( 𠜌 ) 𠜌 = 0 .

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:582181

DOI: 10.1155/2009/582181

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