Abstract
A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend the posner’s result to the case of generalized derivations centralizing on Lie ideals of rings with involution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bell H.E., Martindale W.S. III: Centralizing mappings of semiprime rings. Can. Math. Bull. 30(1), 92–101 (1987)
Divinsky N.: On commuting automorphisms of rings. Trans. Roy. Soc. Can. Sect. III. 3(49), 1922 (1955)
Oukhtite L., Salhi S.: Centralizing automorphisms and Jordan left derivations on σ-prime rings. Adv. Algebra 1(1), 19–26 (2008)
Oukhtite L., Salhi S.: Lie ideals and derivations of σ-prime rings. Int. J. Algebra 1(1), 25–30 (2007a)
Oukhtite L., Salhi S.: σ-Lie ideals with derivations as homomorphisms and anti-homomorphisms. Int. J. Algebra 1(5), 235–239 (2007b)
Oukhtite L., Salhi S., Taoufiq L.: Commutativity conditions on derivations and Lie ideals in σ-prime rings. Beiträge Algebra Geom. 51(1), 275–282 (2010)
Posner E.: Derivations in prime rings. Proc. Am. Math. Soc. 8, 1093–1100 (1957)
Rehman N.: On commutativity of rings with generalized derivations. Math. J. Okayama Univ. 44, 4349 (2002)
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Oukhtite, L. Lie ideals and centralizing generalized derivations of rings with involution. Beitr Algebra Geom 52, 349–355 (2011). https://doi.org/10.1007/s13366-011-0058-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13366-011-0058-2