Commutativity results for semiprime rings with derivations

Mohammad Nagy Daif

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-4

Abstract:

We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [ d ( x ) , d ( y ) ] = 0 for all x , y ∈ R , to the case of semiprime rings. An extension of this result is proved for a two-sided ideal but is shown to be not true for a one-sided ideal. Some of our recent results dealing with U * - and U * * - derivations on a prime ring are extended to semiprime rings. Finally, we obtain a result on semiprime rings for which d ( x y ) = d ( y x ) for all x , y in some ideal U .

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:975420

DOI: 10.1155/S0161171298000660

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