Let ℛ be a prime ring, C{script} the extended centroid of ℛ, ℒ a Lie ideal of ℛ, F be a nonzero generalized skew derivation of ℛ with associated automorphism α, and n ≥ 1 be a fixed integer. If (F(xy)-yx)n = 0 for all x, y ∈ ℒ, then ℒ is commutative and one of the following statements holds: (1) Either ℒ is central; (2) Or ℛ ⊆ M 2(C{script}), the 2 × 2 matrix ring over C{script}, with char(C{script}) = 2. © 2014 Copyright Taylor and Francis Group, LLC.
Generalized Skew Derivations with Nilpotent Values in Prime Rings
DE FILIPPIS, Vincenzo
2014-01-01
Abstract
Let ℛ be a prime ring, C{script} the extended centroid of ℛ, ℒ a Lie ideal of ℛ, F be a nonzero generalized skew derivation of ℛ with associated automorphism α, and n ≥ 1 be a fixed integer. If (F(xy)-yx)n = 0 for all x, y ∈ ℒ, then ℒ is commutative and one of the following statements holds: (1) Either ℒ is central; (2) Or ℛ ⊆ M 2(C{script}), the 2 × 2 matrix ring over C{script}, with char(C{script}) = 2. © 2014 Copyright Taylor and Francis Group, LLC.File in questo prodotto:
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