대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제35권3호
  • /
  • Pages.733-744
  • /
  • 2020
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON GENERALIZED JORDAN DERIVATIONS OF GENERALIZED MATRIX ALGEBRAS

  • Ashraf, Mohammad (Department of Mathematics Aligarh Muslim University) ;
  • Jabeen, Aisha (Department of Applied Sciences & Humanities Jamia Millia Islamia)
  • 투고 : 2019.10.15
  • 심사 : 2020.02.13
  • 발행 : 2020.07.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let 𝕽 be a commutative ring with unity, A and B be 𝕽-algebras, M be a (A, B)-bimodule and N be a (B, A)-bimodule. The 𝕽-algebra 𝕾 = 𝕾(A, M, N, B) is a generalized matrix algebra defined by the Morita context (A, B, M, N, 𝝃MN, ΩNM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.

키워드

과제정보

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.

참고문헌

  1. 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
  2. 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
  3. 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
  4. W. S. Cheung, Mappings on triangular algebras, Ph.D. dissertation, University of Victoria, 2000.
  5. I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. https://doi.org/10.2307/2032688
  6. B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166. https://doi.org/10.1080/00927879808826190
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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.
  12. A. D. Sands, Radicals and Morita contexts, J. Algebra 24 (1973), 335-345. https://doi.org/10.1016/0021-8693(73)90143-9
  13. 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
  14. 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
  15. 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
  16. 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.