Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. Suppose that F is a non-zero b-generalized skew derivation of R, L a non-central Lie ideal of R and n≥1 a fixed positive integer such that (F(x)x)n∈Z(R), for all x∈L. If either char(R)=0 or 0≠char(R)=p≥n+1, then R⊆M2(K), the 2×2 matrix ring over a field K.
Power central valued b-generalized skew derivations on Lie ideals
Rania F.
2024-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. Suppose that F is a non-zero b-generalized skew derivation of R, L a non-central Lie ideal of R and n≥1 a fixed positive integer such that (F(x)x)n∈Z(R), for all x∈L. If either char(R)=0 or 0≠char(R)=p≥n+1, then R⊆M2(K), the 2×2 matrix ring over a field K.File in questo prodotto:
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