Annihilators on co-commutators with generalized derivations on Lie ideals

作者：Carini Luisa^*; De Filippis Vincenzo; Dhara Basudeb

来源：Publicationes Mathematicae-Debrecen, 2010, 76(3-4): 395-409.

• prime rings
• derivations
• generalized derivations
• Utumi quotient rings
• differential identities

Let R be a prime ring of characteristic different 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 not equal a is an element of R such that a(H(u)u - uG(u)) = 0, for all u is an element of L, then one of the following holds:
(1) there exist b', c' is an element of U such that H(x) = b'x + xc', G(x) = c'x with ab' = 0;
(2) R satisfies s(4) and there exist b', c', q' is an element of U such that H (x) = b' x + xc', G(x) = c'x + xq', with a(b' - q') = 0.

• 出版日期2010-4