Volume 69 | Issue 2 | Year 2023 | Article Id. IJMTT-V69I2P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I2P509
Received | Revised | Accepted | Published |
---|---|---|---|
29 Dec 2022 | 02 Feb 2023 | 13 Feb 2023 | 20 Feb 2023 |
In this paper we initiated the study of generalized derivations on Mn×n(C). We characterize all the generalized derivations on Mn×n(C) and proved the sufficient conditions when the product of two generalized derivations is again a derivation.
[1] Edward C. Posner, “Derivation in Prime Rings,” Proceedings of the American Mathematical Society, vol. 8, no. 6, pp. 1093-1100, 1957. Crossref, https://doi.org/10.2307/2032686
[2] Bojan Hvala, “Generalized Derivations in Rings,” Communication in Algebra, vol. 26, no. 4, pp. 1147-1166, 1998. Crossref, https://doi.org/10.1080/00927879808826190
[3] Neset Aydin, “A Note on Generalized Derivations of Prime Rings,” International Journal of algebra, vol. 5, no. 1, pp. 17-23, 2011.
[4] Matej Bresar, “On the Distance of the Composition of Two Derivations to the Generalized Derivations,” Glasgow Mathematical Journal, vol. 33, no. 1, pp. 89-93, 1991. Crossref, https://doi.org/10.1017/S0017089500008077
[5] Richard V. Kadison, “Derivations of Operator Algebras,” Annals of Mathematics, vol. 83, no. 2, pp. 280-293, 1966.
[6] Shoichiro Sakai, “On a Conjecture of Kaplansky,” Tohoku Mathematical Journal, vol. 12, no. 1, pp. 31-33, 1960. Crossref, https://doi.org/10.2748/tmj/1178244484
[7] Shoichiro Sakai, “Derivations of W*-Algebras,” Annals of Mathematics, vol. 83, no. 2, pp. 273-279, 1966.
[8] K.L Kaushik, “Generalized Inner Derivations,” International Journal of Science and Engineering Development Research, vol. 5, no. 8, 2020.
[9] K.L. Kaushik, Generalized Derivations in Non-Associative Algebra, Algebra and Its Applications (Recent Developments) 2011 published by Narosa Publishers Pvt. Ltd. ISBN: 97881-8487-124-1.
[10] N.O. Alshehri, “Generalized Derivations of Lattices,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 13, pp. 629-640, 2010.
[11] Nadeem Ur-Rehman, “On Commutativity of Rings with Generalized Derivations,” Mathematical Journal of Okayama University, vol. 44, 43-49, 2002.
[12] Tsiu-Kwen Lee, “Generalized Derivations of Left Faithful Rings,” Communications in Algebra, vol. 27, no. 8, pp. 4057-4073, 1999. Crossref, https://doi.org/10.1080/00927879908826682
[13] M.A. Quadri, M.S. Khan, and N. Rehman, “Generalized Derivations and Commutativity,” Indian Journal of pure and applied Mathematics, vol. 34, no. 9, pp. 1393-1396, 2003.
[14] Josa Vukman, “A Note on Generalized Derivations of Semiprime Rings,” Taiwanese Journal of Mathematics, vol. 11, no. 2, pp. 367- 370, 2007.
[15] Tsiu-Kwen Lee, and Shiue, W. K. (2001). Identities with generalized derivations.
[16] George F. Leger, and Eugene M. Luks, “Generalized Derivations of Lie Algebras,” Journal of Algebra, vol. 228, no. 1, pp. 165-203, 2000. Crossref, https://doi.org/10.1006/jabr.1999.8250
[17] Mohammad Ashraf, Asma Ali, and Shakir Ali, “Some Commutativity Theorems for Rings with Generalized Derivations,” Southeast Asian Bulletin of Mathematics, vol. 31, no. 3, 2007.
[18] Ö.Gölbaşi, and K. Kaya, “On Lie Ideals with Generalized Derivations,” Siberian Mathematical Journal, vol. 47, pp. 862-866, 2006. Crossref, https://doi.org/10.1007/s11202-006-0094-6
[19] M.N. Daif, M.S. Tammam El-Sayiad, “Multiplicative Generalized Derivations which are Additive,” East West Math, 9(01), 31-37.
[20] G. Hochschild, “Semi-simple Algebras and Generalized Derivations,” American Journal of Mathematics, vol. 64, no. 1, pp. 677-694, 1942.
[21] Wang, Y. (2006, September). Generalized derivations with power-central values on multilinear polynomials. In Algebra Colloquium (Vol. 13, No. 03, pp. 405-410). Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
[22] Runxuan Zhang, and Yongzheng Zhang, “Generalized Derivations of Lie Superalgebras,” Communications in Algebra, vol. 38, no. 10, pp. 3737-3751, 2010. Crossref, https://doi.org/10.1080/00927870903236228
[23] Vincenzo De Filippis, and Onofrio Mario Di Vincenzo, “Vanishing Derivations and Centralizers of Generalized Derivations on Multilinear Polynomials,” Communications in Algebra, vol. 40, no. 6, pp. 1918-1932, 2012. Crossref, https://doi.org/10.1080/00927872.2011.553859
[24] Shakir Ali, “On Generalized∗-Derivations in∗-Rings,” Palestine Journal of Mathematics, vol. 1, pp. 32-37, 2012.
K.L. Kaushik, Praveen Sharma, "Generalized Derivations on Mn×N(C)," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 2, pp. 70-73, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I2P509