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Vanishing power values of commutators with derivations

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Abstract

Let R be a prime ring of char R ≠ 2, let d be a nonzero derivation of R, and let ρ be a nonzero right ideal of R such that [[d(x)x n, d(y)] m , [y, x] s ]t = 0 for all x, y є ρ, where n ≥ 1, m ≥ 0, s ≥ 0, and t ≥ 1 are fixed integers. If [ρ, ρ]ρ ≠ 0 then d(ρ)ρ = 0.

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Authors and Affiliations

  1. Belda College, Belda, 721424, W.B., India

    Basudeb Dhara

  2. Indian Institute of Technology, New Delhi, 110016, India

    R. K. Sharma

Authors
  1. Basudeb Dhara
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  2. R. K. Sharma
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Correspondence to Basudeb Dhara.

Additional information

Original Russian Text Copyright © 2009 Dhara B. and Sharma R. K.

The first author is grateful to the University Grants Commission of India for financial support under Grant F.PSW-156/06-07.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 1, pp. 75–81, January–February, 2009.

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Dhara, B., Sharma, R.K. Vanishing power values of commutators with derivations. Sib Math J 50, 60–65 (2009). https://doi.org/10.1007/s11202-009-0007-6

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  • DOI: https://doi.org/10.1007/s11202-009-0007-6

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