Acknowledgement
This research is supported by Dr. D. S. Kothari Postdoctoral Fellowship under University Grants Commission (Grant No. F.4-2/2006 (BSR)/MA/18-19/0014), awarded to the second author.
References
- M. Ashraf and A. Jabeen, Nonlinear generalized Lie triple derivation on triangular algebras, Comm. Algebra 45 (2017), no. 10, 4380-4395. https://doi.org/10.1080/00927872.2016.1264586
- M. Bresar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), no. 1, 218-228. https://doi.org/10.1016/0021-8693(89)90285-8
- M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), no. 1, 89-93. https://doi.org/10.1017/S0017089500008077
- W. S. Cheung, Mappings on triangular algebras, Ph.D. dissertation, University of Victoria, 2000.
- I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. https://doi.org/10.2307/2032688
- B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166. https://doi.org/10.1080/00927879808826190
- Y. Li, L. van Wyk, and F. Wei, Jordan derivations and antiderivations of generalized matrix algebras, Oper. Matrices 7 (2013), no. 2, 399-415. https://doi.org/10.7153/oam-07-23
- Y. Li and F. Wei, Semi-centralizing maps of generalized matrix algebras, Linear Algebra Appl. 436 (2012), no. 5, 1122-1153. https://doi.org/10.1016/j.laa.2011.07.014
- Y. Li and C. Zheng, A note on Jordan derivations of trivial generalized matrix algebras, Commun. Korean Math. Soc. 32 (2017), no. 2, 261-266. https://doi.org/10.4134/CKMS.c160091
- F. Ma and G. Ji, Generalized Jordan derivations on triangular matrix algebras, Linear Multilinear Algebra 55 (2007), no. 4, 355-363. https://doi.org/10.1080/03081080601127374
- K. Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83-142.
- A. D. Sands, Radicals and Morita contexts, J. Algebra 24 (1973), 335-345. https://doi.org/10.1016/0021-8693(73)90143-9
- J. Vukman, A note on generalized derivations of semiprime rings, Taiwanese J. Math. 11 (2007), no. 2, 367-370. https://doi.org/10.11650/twjm/1500404694
- J. Wu and S. Lu, Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math. 7 (2003), no. 4, 605-613. https://doi.org/10.11650/twjm/1500407580
- Z. Xiao and F. Wei, Commuting mappings of generalized matrix algebras, Linear Algebra Appl. 433 (2010), no. 11-12, 2178-2197. https://doi.org/10.1016/j.laa.2010.08.002
- W. Y. Yu and J. H. Zhang, Generalized Jordan derivations of full matrix algebras, J. Shandong Univ. Nat. Sci. 45 (2010), no. 4, 86-89.