Let R be a prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C, L a non-central Lie ideal of R, F a non-zero b- generalized derivation of R and δ a non-zero derivation of R, such that [F(u), δ(u)] = 0, for all u ∈ L. Then F is a derivation of R and there exists λ ∈ C such that F = λδ, unless when R satisfies the standard identity s4(x1, . . . , x4).
On a quadratic differential identity with b-generalized derivations
Rania F.
2024-01-01
Abstract
Let R be a prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C, L a non-central Lie ideal of R, F a non-zero b- generalized derivation of R and δ a non-zero derivation of R, such that [F(u), δ(u)] = 0, for all u ∈ L. Then F is a derivation of R and there exists λ ∈ C such that F = λδ, unless when R satisfies the standard identity s4(x1, . . . , x4).File in questo prodotto:
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