Let R be a prime ring, H a nonzero generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that there exists such that a(u (s) H(u)u (t) ) (n) = 0 for all , where s a parts per thousand yen 0, t a parts per thousand yen 0, n a parts per thousand yen 1 are fixed integers. Then s = 0, H(x) = bx for all with ab = 0, unless R satisfies s (4), the standard identity in four variables. We also describe completely this last case.
Power Values of Generalized Derivations with Annihilator Conditions in Prime Rings
DE FILIPPIS, Vincenzo;SCUDO, GIOVANNI
2013-01-01
Abstract
Let R be a prime ring, H a nonzero generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that there exists such that a(u (s) H(u)u (t) ) (n) = 0 for all , where s a parts per thousand yen 0, t a parts per thousand yen 0, n a parts per thousand yen 1 are fixed integers. Then s = 0, H(x) = bx for all with ab = 0, unless R satisfies s (4), the standard identity in four variables. We also describe completely this last case.File in questo prodotto:
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