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EnglishLet R be a non-commutative prime ring, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F≠ 0 an b-generalized skew derivation of R, L a non-central Lie ideal of R, 0 ≠ a∈ R and n≥ 1 a fixed integer. In this paper, we prove the following two results:1.If R has characteristic different from 2 and 3 and a[ F(x) , x] n= 0 , for all x∈ L, then either there exists an element λ∈ C, such that F(x) = λx, for all x∈ R or R satisfies s4(x1, … , x4) , the standard identity of degree 4, and there exist λ∈ C and b∈ Q, such that F(x) = bx+ xb+ λx, for all x∈ R.2.If char (R) = 0 or char (R) > n and a[ F(x) , x] n∈ Z(R) , for all x∈ R, then either there exists an element λ∈ C, such that F(x) = λx, for all x∈ R or R satisfies s4(x1, … , x4). © 2018, Springer International Publishing AG, part of Springer Nature.
| Titolo: | b-Generalized Skew Derivations on Lie Ideals |
| Autori: | |
| Data di pubblicazione: | 2018 |
| Rivista: | |
| Abstract: | Let R be a non-commutative prime ring, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F≠ 0 an b-generalized skew derivation of R, L a non-central Lie ideal of R, 0 ≠ a∈ R and n≥ 1 a fixed integer. In this paper, we prove the following two results:1.If R has characteristic different from 2 and 3 and a[ F(x) , x] n= 0 , for all x∈ L, then either there exists an element λ∈ C, such that F(x) = λx, for all x∈ R or R satisfies s4(x1, … , x4) , the standard identity of degree 4, and there exist λ∈ C and b∈ Q, such that F(x) = bx+ xb+ λx, for all x∈ R.2.If char (R) = 0 or char (R) > n and a[ F(x) , x] n∈ Z(R) , for all x∈ R, then either there exists an element λ∈ C, such that F(x) = λx, for all x∈ R or R satisfies s4(x1, … , x4). © 2018, Springer International Publishing AG, part of Springer Nature. |
| Handle: | http://hdl.handle.net/11570/3150094 |
| Appare nelle tipologie: | 14.a.1 Articolo su rivista |
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