Abstract
In this paper, we investigate commutativity of rings with involution in which derivations satisfy certain algebraic identities on Jordan ideals. Moreover, we extend some results for derivations of prime rings to Jordan ideals. Furthermore, an example is given to prove that the ∗-primeness hypothesis is not superfluous.
Article PDF
Similar content being viewed by others
References
Awtar R.: Lie and Jordan structure in prime rings with derivations. Proc. Amer. Math. Soc 41, 67–74 (1973)
Bell H.E., Daif M.N.: On derivations and commutativity in prime rings. Acta Mathematica Hungarica 66, 337–343 (1995)
Daif M.N., Bell H.E.: Remarks on derivations on semiprime rings. Int. J. Math. Math. Sci 15, 205–206 (1992)
Oukhtite L.: Posner’s second theorem for Jordan ideals in rings with involution. Expo. Math. 29(4), 415–419 (2011)
Oukhtite L.: On Jordan ideals and derivations in rings with involution. Comment. Math. Univ. Carol. 51(3), 389–395 (2010)
Oukhtite L., Salhi S.: On derivations in σ-prime rings. Int. J. Algebra 1(5), 241–246 (2007)
Oukhtite L., Salhi S.: On commutativity of σ-prime rings. Glas. Mat. Ser. III 41(1), 57–64 (2006)
Oukhtite, L.; Mamouni, A.: Generalized derivations centralizing on Jordan ideals of rings with involution. submitted
Zaidi S.M.A., Ashraf M., Ali S.: On Jordan ideals and left (θ,θ)-derivations in prime rings. Int. J. Math. Math. Sci. 2004(37), 1957–1969 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Oukhtite, L., Mamouni, A. Derivations satisfying certain algebraic identities on Jordan ideals. Arab. J. Math. 1, 341–346 (2012). https://doi.org/10.1007/s40065-012-0039-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-012-0039-9