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Annihilator condition of a pair of derivations in prime and semiprime rings

Author

Listed:
  • Basudeb Dhara

    (Belda College)

  • Nurcan Argaç

    (Ege University)

  • Krishna Gopal Pradhan

    (Belda College)

Abstract

Let n be a fixed positive integer, R be a prime ring, D and G two derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(D(u)u n −u n G(u)) = 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then one of the following holds: 1. D = G = 0, unless R satisfies s 4; 2. char (R) ≠ 2, R satisfies s 4, n is even and D = G; 3. char (R) ≠ 2, R satisfies s 4, n is odd and D and G are two inner derivations induced by b, c respectively such that b + c ∈ C; 4. char (R) = 2 and R satisfies s 4. We also investigate the case when R is a semiprime ring.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:1:d:10.1007_s13226-015-0166-z
    DOI: 10.1007/s13226-015-0166-z
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    References listed on IDEAS

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    1. Kyoo-Hong Park & Yong-Soo Jung & Jae-Hyeong Bae, 2002. "Derivations in Banach algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-5, January.
    2. 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.
    3. 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.
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    1. 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.

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