Let R be a non-commutative prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring and C its extended centroid. Suppose that L is a non-central Lie ideal of R, F a nonzero b-generalized skew derivation of R. If [[F(x),x],F(x)] Z(R), for all x L, then one of the following holds: (a) there exists λ C such that F(x) = λx, for all x R; (b) R ⊆ M2(C), the ring of 2 × 2 matrices over C, and there exist a Qr and λ C such that F(x) = ax + xa + λx, for all x R.
On Posner's theorem with b -generalized skew derivations on Lie ideals
Carini L.
Primo
;Scudo G.Secondo
2023-01-01
Abstract
Let R be a non-commutative prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring and C its extended centroid. Suppose that L is a non-central Lie ideal of R, F a nonzero b-generalized skew derivation of R. If [[F(x),x],F(x)] Z(R), for all x L, then one of the following holds: (a) there exists λ C such that F(x) = λx, for all x R; (b) R ⊆ M2(C), the ring of 2 × 2 matrices over C, and there exist a Qr and λ C such that F(x) = ax + xa + λx, for all x R.File in questo prodotto:
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