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Annihilator condition on power values of derivations

Author

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  • Basudeb Dhara

    (Belda College)

Abstract

Let R be a prime ring, d, δ two derivations of R, L a noncentral Lie ideal of R and 0 ≠ a ∈ R. The main object in this paper is to discuss the situations a (d (x)x − xδ (x)) n = 0 for all x ∈ L and a (d (x)x − xδ (x)) ∈ Z (R) for all x ∈ L, where n ≥ 1 is a fixed integer.

Suggested Citation

  • Basudeb Dhara, 2011. "Annihilator condition on power values of derivations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(5), pages 357-369, October.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:5:d:10.1007_s13226-011-0023-7
    DOI: 10.1007/s13226-011-0023-7
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    References listed on IDEAS

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    1. Nurcan Argac & Vincenzo Filippis, 2010. "Cocentralizing derivations and nilpotent values on Lie ideals," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(3), pages 475-483, June.
    2. Basudeb Dhara, 2009. "Vanishing Power Values of Commutators with Derivations on Prime Rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-8, January.
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    Cited by:

    1. Basudeb Dhara & Nurcan Argaç & Krishna Gopal Pradhan, 2016. "Annihilator condition of a pair of derivations in prime and semiprime rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 111-124, March.

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    1. Basudeb Dhara & Nurcan Argaç & Krishna Gopal Pradhan, 2016. "Annihilator condition of a pair of derivations in prime and semiprime rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 111-124, March.

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