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- Title
On Posner's theorem with b-generalized skew derivations on Lie ideals.
- Authors
Carini, Luisa; Scudo, Giovanni
- Abstract
Let R be a non-commutative prime ring of characteristic different from 2 and 3, Q r 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) = λ x , for all x ∈ R ; (b) R ⊆ M 2 (C) , the ring of 2 × 2 matrices over C, and there exist a ∈ Q r and λ ∈ C such that F (x) = a x + x a + λ x , for all x ∈ R.
- Subjects
LIE algebras; NONCOMMUTATIVE rings; QUOTIENT rings
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 3, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823500573