Characterization of prime rings having involution and centralizers
DOI:
https://doi.org/10.22199/issn.0717-6279-5897Keywords:
prime ring, left centralizer, involutionAbstract
The major goal of this paper is to study the commutativity of prime rings with involution that meet specific identities using left centralizers. The results obtained in this paper are the generalization of many known theorems. Finally, we provide some examples to show that the conditions imposed in the hypothesis of our results are not superfluous.
References
S. Ali and N. A. Dar, “On centralizers of prime rings having involution”, Bulletin of the Iranian Mathematical Society, vol. 41, pp. 1465-1475, 2015.
A. Ali and M. Yasen, “A note on automorphisms of prime and semiprime rings”, Kyoto Journal of Mathematics, vol. 45., pp. 243-246, 2005. https://doi.org/10.1215/kjm/1250281987
M. Ashraf and S. Ali, “On left multipliers and the commutativity of prime rings”, Demonstratio Mathematica, vol. 41, pp. 764-771, 2008. https://doi.org/10.1515/dema-2013-0125
N. Divinsky, “On commuting automorphisms of rings”, Trans. Roy. Soc. Canada. Sect. III, vol. 49, pp. 19-22, 1955.
I. R. Hentzel and T. El-Sayiad, “Left centralizers of rings that are not semiprime”, Rocky Mountain Journal of Mathematics, vol. 41, pp. 1471-1482, 2011. https://doi.org/10.1216/RMJ-2011-41-5-1471
I. N. Herstein, Rings with involution. Chicago: University of Chicago press, 1976.
J. Luh, “A note on automorphisms of rings”, The American Mathematical Monthly, vol. 77, pp. 61-62, 1970. https://doi.org/10.1080/00029890.1970.11992420
B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, “Commutativity theorems in rings having involution”, Communications in Algebra, vol. 45, pp. 698-708, 2017. https://doi.org/10.1080/00927872.2016.1172629
E. C. Posner, “Derivations in prime rings”, Proceedings of the American Mathematical Society, vol. 8, pp. 1093-1100, 1957.
M. F. Smiley, “Remarks on commuting automorphisms”, The American Mathematical Monthly, vol. 63, pp. 466-470, 1956.
J. Vukman, “Centralizer on semiprime rings”, Commentationes Mathematicae Universitatis Carolinae, vol. 42, pp. 237-245, 2001.
J. Vukman and K. U. Irena, “On centralizers of semiprime rings having involution”, Studia Scientiarum Mathematicarum Hungarica, vol. 41, pp. 61-67, 2006. https://doi.org/10.1556/sscmath.43.2006.1.4
B. Zalar, “On centralizer of semiprime rings”, Commentationes Mathematicae Universitatis Carolinae, vol. 32, pp. 609-614, 1991.
Published
How to Cite
Issue
Section
Copyright (c) 2023 Nadeem Ahmad Dar, Adnan Abbasi, Claus Haetinger, Arshad Madni, Muzibur Rahman Mozumder

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.