Annihilating and power-commuting generalized skew derivations on lie ideals in prime rings

Title:

Annihilating and power-commuting generalized skew derivations on lie ideals in prime rings

Creator:

De Filippis, Vincenzo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1605fd06-41d5-416a-af43-77d3c331d40b
uuid:1605fd06-41d5-416a-af43-77d3c331d40b
issn:0011-4642

Subject:

matematika, derivace funkce, mathematics, derivatives (mathematics), generalized skew derivation, Lie ideal, prime ring, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let R be a prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R. An additive map D: R → R is called an α-derivation (or a skew derivation) on R if D(xy) = D(x)y + α(x)D(y) for all x, y \in R. An additive mapping F: R → R is called a generalized α-derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F(xy) = F(x)y + α(x)D(y) for all x, y \in R. We prove that, if F is a nonzero generalized skew derivation of R such that F(x)×[F(x), x]n = 0 for any x \in L, then either there exists λ \in C such that F(x) = λx for all x \in R, or R\subset M_{2}\left ( C \right ) and there exist a \in Qr and λ \in C such that F(x) = ax + xa + λx for any x \in R., Vincenzo De Filippis., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

481-492

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:2

Harvested from:

CDK

Metadata only:

false