A characterization of σ-prime rings involving generalized derivations
DOI:
https://doi.org/10.22199/issn.0717-6279-6412Keywords:
σ-prime ring, derivation, involution, generalized derivationAbstract
This paper’s major goal is to work on commutativity of σ-prime rings with second kind involution σ, involving generalized derivation satisfy the certain differential identities. Finally, we provide some examples to demonstrate that the conditions assumed in our results are not unnecessary
Downloads
References
S. Ali and N.A.Dar,"On∗-centralizing mappings in rings with invo-lution",Georgian Math. J., Vol. 1, pp. 25-28, 2014. https://doi.org/10.1515/gmj-2014-0006
A. Alahmadi, H. Alhazmi, S. Ali, and A. N. Khan,"Additive maps onprime and semiprime rings with involution",Hacet. J. Math. Stat,Vol.49 (3), pp. 1126-1133, 2020. https://doi.org/10.15672/hujms.661178
M.Ashraf,andM.A.Siddeeque,"Posnersfirst theorem for *-ideals inprime rings with involution"Kyungpook Math. J., Vol. 56, pp. 343-347,2016. https://doi.org/10.5666/KMJ.2016.56.2.343
M. N. Daif, "Commutativity results for semiprime rings with deriva-tion,Int. J. Math. Math. Sci, Vol. 21 (3), pp. 471-474, 1998. https://doi.org/10.1155/S0161171298000660
I. N. Herstein, "Rings with involution",University of Chicago Press,Chicago, 1976.
M. S. Khan, S. Ali, and A. Khan, "On∗-ideals and derivations inprime rings with involution",The Aligarh Bull. Math., Vol. 37 (2), pp.59-70, 2018.
C. Lanski, "Differential identities, Lie ideals, and Posner's theorems",Pacific J. Math., Vol. 134 (2), pp. 275-297, 1988. https://doi.org/10.2140/pjm.1988.134.275
P. H Lee, and T. K. Lee, "On derivations of prime rings",Chines J.Math., Vol. 9 (2), pp. 107-110, 1981.
B. Nejjar, A. Kacha, A. Mamouni, and L. Oukhtite, "Commutativitytheorems in rings with involution",Comm. Algebra, Vol. 45 (2), pp.698-708, 2017. https://doi.org/10.1080/00927872.2016.1172629
L. Oukhtite, and O. Ait Zemzami, "A study of differential prime ringswith involution",Georgian Math. J., Vol. 28 (1), pp. 133-139, 2021. https://doi.org/10.1515/gmj-2019-2061
J. H. Mayne, "Centralizing mappings of prime rings",Canad. Math.Bull., Vol. 27, pp. 122-126, 1984. https://doi.org/10.4153/CMB-1984-018-2
M. A. Idrissi, A. Mamouni, and L. Oukhtite, "On generalized deriva-tions and commutativity of prime rings with involution",De Gruyter, pp. 91-100, 2018. https://doi.org/10.1515/9783110542400-008
L. Oukhtite, A. Mamouni, "Generalized derivations centralizing onJordan ideals of rings with involution",Turkish J. Math.,Vol.38,pp.225-232, 2014. https://doi.org/10.3906/mat-1203-14
E. C. Posner, "Derivations in prime rings",Proc. Amer. Math. Soc.,Vol. 8, pp. 1093-1100, 1957. https://doi.org/10.1090/S0002-9939-1957-0095863-0
F. Rania, "Generalized derivations with skew-commutativity condi-tions on polynomials in prime rings",Beitrage zur Algebra und Ge-ometrie/Contributions to Algebra and Geometry, Vol. 60, pp. 513-525,2019.
F. Rania, G. Scudo, A quadratic differential identity with generalizedderivations on multilinear polynomials in prime rings,MediterraneanJournal of Mathematics, Vol. 11, pp. 273-285, 2014. https://doi.org/10.1007/s13366-018-0424-4
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Wasim Ahmed, Md. Arshad Madni, Muzibur Rahman Mozumder, Abu Zaid Ansari
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.
