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Power Values of Generalized Derivations with Annihilator Conditions in Prime Rings |
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| Authors: | Basudeb Dhara Vincenzo De Filippis Giovanni Scudo |
| Affiliation: | 1. Belda College, Belda, Paschim Medinipur, 721424, India 2. Dipartimento di Scienze per l’Ingegneria e per l’Architettura, Università di Messina, 98166, Messina, Italy 3. Dipartimento di Matematica, Università di Messina, 98166, Messina, Italy |
| Abstract: | Let R be a prime ring, H a nonzero generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that there exists ${0 neq a in R}$ such that a(u s H(u)u t ) n = 0 for all ${u in L}$ , where s ≥ 0, t ≥ 0, n ≥ 1 are fixed integers. Then s = 0, H(x) = bx for all ${x in R}$ with ab = 0, unless R satisfies s 4, the standard identity in four variables. We also describe completely this last case. |
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