On ∗-reverse derivable maps
DOI:
https://doi.org/10.22199/issn.0717-6279-5905Keywords:
additivity, reverse derivable maps, involution, Peirce decompositionAbstract
Let R be a ring with involution containing a nontrivial symmetric idempotent element e. Let δ : R → R be a mapping such that δ(ab) = δ(b)a∗ + b∗δ(a) for all a, b ∈ R, we call δ a ∗−reverse derivable map on R. In this paper, our aim is to show that under some suitable restrictions imposed on R, every ∗−reverse derivable map of R is additive.
References
M. Bresăr, and J. Vukman, “Jordan derivations on prime rings”, Bull. Aust. Math. Soc., vol. 37, no. 3, pp. 321-322, 1988.
M. Bresăr, and J. Vukman, “Jordan (θ, φ)-derivations”, Glas. Mat. Ser. III, vol. 26, no. 1-2, pp. 13-17, 1991.
M. N. Daif, “When is a multiplicative derivation additive?”, Internat. J. Math. Math. Sci., vol. 14, no. 3, pp. 615-618, 1991.
M. N. Daif, and M. S. Tammam-El-Sayiad, “Multiplicative generalized derivations which are additive”, East-West J. Math., vol. 9, no. 1, pp. 31-37, 2007.
D. Eremita, and D. Ilisevic, “On additivity of centralisers”, Bull. Aust. Math. Soc., vol. 74, pp. 177-184, 2006.
B. L. M. Ferreira, “Jordan elementary maps on alternative division rings”, Serdica Math. Journal, vol. 43, pp. 161-168, 2017.
R. N. Ferreira, and B. L. M. Ferreira, “Jordan derivation on alternative rings”, International Journal of Mathematics, Game Theory, and Algebra, vol. 25, pp. 435-444, 2017.
R. N. Ferreira, and B. L. M. Ferreira, “Jordan triple derivation on alternative rings”, Proyecciones (Antofagasta), vol. 37, pp. 169-178, 2018.
B. L. M. Ferreira, J. C. M. Ferreira, and H. Guzzo Jr., “Jordan maps on alternative algebras”, JP Journal of Algebra, Number Theory and Applications, vol. 31, pp. 129-142, 2013.
B. L. M. Ferreira, J. C. M. Ferreira, and H. Guzzo Jr., “Jordan Triple Elementary Maps on Alternative Rings”, Extracta Mathematicae, vol. 29, pp. 1-18, 2014.
B. L.M. Ferreira, J. C. M. Ferreira, H. Guzzo Jr., “Jordan Triple Maps of Alternative algebras”, JP Journal of Algebra, Number Theory and Applications, Vol. 33, pp. 25-33, 2014.
J. M. Ferreira, B. L. M. Ferreira, “Additivity of n−multiplicative maps on alternative rings”, Commun. Algebra, vol. 44, pp. 1557-1568, 2016.
B. L. M. Ferreira, R. Nascimento, “Derivable maps on alternative rings”, Recen, vol. 16, pp. 1-5, 2014.
I. N. Herstein, “Jordan derivations of prime rings”, Proc. Amer. Math. Soc., vol. 8, pp. 1104-1110, 1957.
N. Jacobson, Structure of Rings, Amer. Math. Soc., U.S.A., 1964.
W. Jing, F. Lu, “Additivity of Jordan (triple) derivations on rings”, Commun. Algebra, vol. 40, pp. 2700-2719, 2012.
P. Li, F. Lu, “Additivity of elementary maps on rings”, Commun. Algebra, vol. 32, no. 10, pp. 3725-3737, 2004.
W. S. Martindale III, “When are multiplicative mappings additive?”, Proc. Amer. Math. Soc., vol. 21, pp. 695-698, 1969.
Y. Wang, “The additivity of multiplicative maps on rings”, Commun. Algebra, vol. 37, pp. 2351-2356, 2009.
Published
How to Cite
Issue
Section
Copyright (c) 2023 Bruno L. M. Ferreira, Gurninder Sandhu
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
