Let R be prime ring with characteristic different from 2, C denotes the extended centroid, L a Lie ideal of R and Qr the right Martindale quotient of the ring R. Let Δ1 and Δ2 represents two generalized skew derivations of R associated with (ψ,l1) and (ψ,l2), respectively, such that ψ.l1=l1.ψ and ψ.l2=l2.ψ. If, for every r∈L, Δ12(r)r=Δ2(r2), then we characterize the maps Δ1 and Δ2. As an application of this generalization, we proved that if Δ1(τ2)=0 for all τ∈R, then R contains a non-zero central ideal.
Generalized skew derivations on Lie ideals in prime rings
Scudo, Giovanni
;
2025-01-01
Abstract
Let R be prime ring with characteristic different from 2, C denotes the extended centroid, L a Lie ideal of R and Qr the right Martindale quotient of the ring R. Let Δ1 and Δ2 represents two generalized skew derivations of R associated with (ψ,l1) and (ψ,l2), respectively, such that ψ.l1=l1.ψ and ψ.l2=l2.ψ. If, for every r∈L, Δ12(r)r=Δ2(r2), then we characterize the maps Δ1 and Δ2. As an application of this generalization, we proved that if Δ1(τ2)=0 for all τ∈R, then R contains a non-zero central ideal.File in questo prodotto:
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