Annihilators on co-commutators with generalized derivations on Lie ideals

• Autores: Luisa Carini, Vincenzo De Filippis, Basudeb Dhara
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 76, Fasc. 3-4, 2010, págs. 395-409
• Idioma: inglés
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• Resumen

  • Let R be a prime ring of characteristic di®erent from 2, U the Utumi quotient ring of R, C = Z(U) the extended centroid of R, L a non-central Lie ideal of R, H and G non-zero generalized derivations of R. Suppose that there exists 0 6= a 2 R such that a(H(u)u ¡ uG(u)) = 0, for all u 2 L, then one of the following holds:

    (1) there exist b0; c0 2 U such that H(x) = b0x+xc0, G(x) = c0x with ab0 = 0;

    (2) R satis¯es s4 and there exist b0; c0; q0 2 U such that H(x) = b0x + xc0, G(x) = c0x + xq0, with a(b0 ¡ q0) = 0.