Let R be a prime ring, with no nonzero nil right ideal, Q the two-sided Martindale quotient ring of R, F a generalized derivation of R, L a noncommutative Lie ideal of R, and b is an element of Q. If, for any u, w is an element of L, there exists n = n(u, w) >= 1 such that (F(uw)-bwu)(n) = 0, then one of the following statements holds: (a) F = 0 and b = 0; (b) R subset of M-2(K), the ring of 2 x 2 matrices over a field K, b(2) = 0, and F(x)= -bx, for all x is an element of R.
Subsets with Generalized Derivations Having Nilpotent Values on Lie Ideals
DE FILIPPIS, Vincenzo;SCUDO, GIOVANNI
2016-01-01
Abstract
Let R be a prime ring, with no nonzero nil right ideal, Q the two-sided Martindale quotient ring of R, F a generalized derivation of R, L a noncommutative Lie ideal of R, and b is an element of Q. If, for any u, w is an element of L, there exists n = n(u, w) >= 1 such that (F(uw)-bwu)(n) = 0, then one of the following statements holds: (a) F = 0 and b = 0; (b) R subset of M-2(K), the ring of 2 x 2 matrices over a field K, b(2) = 0, and F(x)= -bx, for all x is an element of R.File in questo prodotto:
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