Generalized derivations as homomorphisms or anti-homomorphisms on Lie ideals

Let R be a prime ring of char(R)≠2, Z the center of R, and L a nonzero Lie ideal of R. If R admits a generalized derivation F associated with a derivation d which acts as a homomorphism or as anti-homomorphism on L, then either d=0 or L⊆Z. This result generalizes a theorem of Wang and You.

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Published in:Arab journal of mathematical sciences 2016-01, Vol.22 (1), p.22-28
Main Authors: ur Rehman, Nadeem, Raza, Mohd Arif
Format: Article
Language:English
Subjects:
Generalized derivations
Homomorphisms and anti-homomorphisms
Lie ideal
Martindale ring of quotients
Prime ring
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description Let R be a prime ring of char(R)≠2, Z the center of R, and L a nonzero Lie ideal of R. If R admits a generalized derivation F associated with a derivation d which acts as a homomorphism or as anti-homomorphism on L, then either d=0 or L⊆Z. This result generalizes a theorem of Wang and You.
doi_str_mv 10.1016/j.ajmsc.2014.09.001
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subjects Generalized derivations
Homomorphisms and anti-homomorphisms
Lie ideal
Martindale ring of quotients
Prime ring
title Generalized derivations as homomorphisms or anti-homomorphisms on Lie ideals
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